**Jozef Henryk Przytycki**

Curriculum Vitae

November, 2009

**Office Address:** Department of Mathematics, GWU

George Washington University

Washington, DC 20052, USA

**e-mail** przytyck@gwu.edu

**tel.** (202) 994-6238

**Fax: **(202) 994-6760

**Personal Data:**

**Born:** October 1953, Warsaw Poland, Married June 1984 to Teresa M.

Szczepanek, 2 children: Tomasz born November, 1987 and Pawe l born

December, 1989.

**Research interest:**

primary : Classical knot theory, topology and geometry of 3-manifolds, algebraic

topology based on knots (subject class: 57).

secondary: Graph theory, hyperbolic geometry, 4-manifolds, statistical
mechanics,

representations of Lie algebras and Hopf algebras (quantum groups),

Hecke algebras, character varieties, symplectic structures, Hochschild

homology, cyclic homology and history of mathematics.

**Education:** **M.Sc.** Warsaw University, Department of Mathematics,
Computer Science and Mechanics, 1977.

thesis: “Actions of Zn-groups on 3-manifolds”.

**
Ph.D. ** Columbia University, 1981, thesis: “Incompressible surfaces in
3-manifolds”

thesis advisor: Professor Joan Birman

**
Habilitation **Warsaw University, December 1994.

Topic: “Invariants of knots in 3-manifolds”

Distinctions:

(a) Fellow of Washington Academy of Sciences (WAS); Elected 2005.

(b) The Oscar and Shoshana Trachtenberg Prize for Research Scholarship for 2005.

(c) Columbian research fellow (GWU), 2003-2004,

(d) GWU award for the Exemplary Paper in the Natural, Mathematical, and Biological sciences,

for 1996-1997,

(e) The first Pulikowski’s Lecture, Pozna´n, March 1994.

(f) Member of the Institute for Advanced Study (Spring semester of 1990).

(g) Lecture notes (“Topology of 3-dimensional manifolds”) won the prize of the President of the

Warsaw University, 1989;

(h) Winner of Kuratowski Prize for young mathematicians (1982)

(i) Master thesis (later published, see [1]) won the first prize for student paper in the Polish Math-

ematical Society Competition (Marcinkiewicz’s prize), 1977;

(j) Rector’s Prize for top students, Warsaw University, (several times, 1972-1977).

(k) Three times prize winner (top eight) in Polish Math. Olympiad. Once in the third prize group

(bronze medal) in International Mathematical Olympiad (1971);

Who’sWho

I.Marquis Who’sWho (several times) e.g.:

(1) Who’sWho in the World the 25th Silver edition, 2008, November 2007

(2) Who’sWho in America, 2009 (110th Anniversary Edition),

(3) Who’s Who in Science and Engineering, 10th Anniversary Edition, 2008-2009, December 2007.

(4) Who’s Who in American Education, 8th Edition, 2007-2008, August 2007.

II. Entry in 2000 outstanding intellectuals of the 21st Century,

First edition, 2002; International Biographical Centre, Cambridge CB2 3QP England Ed. Ross

Hilton, pp.404-405.

2

Membership in Professional Organizations:

1. American Mathematical Society (AMS),

2. The Mathematical Association of America (MAA),

3. American Association for the Advancement of Science (AAAS),

4. New York Academy of Sciences (NYAS),

5. Washington Academy of Sciences (WAS)

6. The Polish Institute of Arts & Sciences of America (PIASA)

7. Polish Mathematical Society (PTM).

Employment:

1977-1982 Warsaw University (Poland), Assistant;

1982-1988 Permanent position:

Warsaw University (Poland), Adjunkt (Assistant Professor);

(i) University of British Columbia, Visiting Assistant Professor, 1986-1987,

(ii) Toronto University, Postdoctoral Fellow, 1987-1988.

1988-1989 University of British Columbia, Visiting Associate Professor,

1989-1990 Michigan State University, Visiting Scholar, Fall semester of 1989 and Institute for Advanced

Study (Princeton), Member, Spring semester of 1990.

1990-1992 University of California at Riverside, Associate visiting professor/visiting scholar,

(i) University of Tennessee, Knoxville TN, October-November 1991.

1992-1994 Odense University (Denmark), Lecturer (Associate professor)/visiting scholar).

(i) Warsaw University (Poland), Fall semester of 1993.

(ii) Gottingen (Germany), February 1994.

(iii) Luis Pasteur University, Strasbourg, France, April-May 1994.

1994-1995 University of California at Berkeley, Visiting Associate Research Mathematician.

Permanent position:

(i) 1995- 1997 George Washington University, Assistant Professor.

(ii) 1997- 1999 George Washington University, Associate Professor.

(iii) 1999 - present George Washington University, Professor.

Sabbatical 1999-2000 University of Maryland, College Park, and:

1. Japan (TWCU) June - August 1999.

2. England (Warwick University), November 1999.

3. Poland (Warsaw University), February - May 2000.

Columbian Research Fellowship, 2003-2004

Sabbatical 2006-2007

University of Maryland, College Park, and:

1. Poland (Warsaw and Gdansk Universities), November-December, 2006;

2. Poland (Warsaw and Gdansk Universities), February-March, 2007;

3. Banff, Canada, April, 2007;

4. Trieste, Italy, May, 2007;

5. Tokyo and Nagoya, Japan, June, 2007;

Editing

Editor of four research journals:

(i) Editor of International Journal of Geometry and Topology, from May of 2008;

http://www.serialspublications.com/journals1.asp?jid=175&jtype=1 .

(ii) Editor of Involve (from 2007);

http://pjm.math.berkeley.edu/inv/about/cover/cover.html

(iii) Editor (member of the Editorial Board) of the Journal Fundamenta Mathematicae, (from

February 2004); http://journals.impan.gov.pl/fm/

(iv) An Associate Editor of the Journal of the Knot Theory and its Ramifications

(from November 1995); http://www.worldscinet.com/jktr/jktr.shtml

Editor of special volumes (14 published and 5 in press or in preparation):

(19) Co-editor (with S.Jablan, L.Kauffman and S.S.Lambropoulou) Proceedings of the Advanced

School and Conference on Knot Theory and its Applications to Physics and Biology at the

International Centre for Theoretical Physics, Trieste, Italy, in World Scietific Series on Knots

and Everything, Vol. (not decided yet), to appear 2010 or 2011 (in preparation).

(18) Co-editor (with M.Dabkowski, V.Harizanov, L.Kauffman and V. Ramakrishna) Proceedings of

Workshop on Knots and quantum computing, University of Texas at Dallas, Volume 2, Jour.

Knot Theory Ram., January 2011, in preparation.

(17) Co-editor (with M.Dabkowski, V.Harizanov, L.Kauffman and V. Ramakrishna) Proceedings of

Workshop on Knots and quantum computing, University of Texas at Dallas, Volume 1, Jour.

Knot Theory Ram., June 2010, in preparation.

(16) Co-editor (with Sofia Lambropoulou), Proceedings of International Conference Knots in Wash-

ington XX; 60th birthday of Louis H. Kauffman; Volume 6,

in World Scientific Series on Knots and Everything, Vol. (not decided yet), to appear 2011 (in

preparation).

(15) Co-editor (with S.King, L.Kauffman, V.Manturov) Proceedings of International Workshop on

“Invariants in Low Dimensional Topology” in Oberwolfach, Germany, Volume 3, Jour. Knot

Theory Ram., February 2010, in preparation.

(14) Co-editor (with S.King, L.Kauffman, V.Manturov) Proceedings of International Workshop on

“Invariants in Low Dimensional Topology” in Oberwolfach, Germany, Volume 2, Jour. Knot

Theory Ram., October 2009, to appear.

(13) Co-editor (with S.King, L.Kauffman, V.Manturov) Proceedings of International Workshop on

“Invariants in Low Dimensional Topology” in Oberwolfach, Germany, Volume 1, Jour. Knot

Theory Ram., June 2009, 160+ ix pages.

(12) Co-editor (with Sofia Lambropoulou), Proceedings of International Conference Knots in Wash-

ington XX; 60th birthday of Louis H. Kauffman; Volume 5, Jour. Knot Theory Ram., 16(10),

December 2007, 211 + xi pages

(11) Co-editor (with Sofia Lambropoulou), Proceedings of International Conference Knots in Wash-

ington XX; 60th birthday of Louis H. Kauffman; Volume 4. Jour. Knot Theory Ram., 16(7),

September 2007, 159 + xii pages.

(10) Co-editor (with Sofia Lambropoulou), Proceedings of International Conference Knots in Wash-

ington XX; 60th birthday of Louis H. Kauffman; Volume 3. Jour. Knot Theory Ram., 16(3),

March 2007, 135 + viii pages.

(9) Co-editor (with Sofia Lambropoulou), Proceedings of International Conference Knots in Wash-

ington XX; 60th birthday of Louis H. Kauffman; Volume 2. Jour. Knot Theory Ram., 15(8),

October 2006, 158 + v pages.

(8) Co-editor (with Sofia Lambropoulou), Proceedings of International Conference Knots in Wash-

ington XX; 60th birthday of Louis H. Kauffman; Volume 1. In Jour. Knot Theory Ram., 15(6),

August 2006, 151 + xii pages.

(7) Co-editor (with V.F.R.Jones, V. Turaev, B.Wajnryb), Proceedings of International Conference

“Knots in Poland 2003”, Volume 3, Fundamenta Mathematicae, 190, June 2006, 297 pages.

(6) Co-editor (with V.F.R.Jones, V. Turaev, B.Wajnryb), Proceedings of International Conference

“Knots in Poland 2003”, Volume 2, Fundamenta Mathematicae, 188, December 2005, 340 pages.

(5) Co-editor (with V.F.R.Jones, V. Turaev, B.Wajnryb), Proceedings of International Conference

“Knots in Poland 2003”, Volume 1, Fundamenta Mathematicae, 184, December 2004, 353 pages.

(4) Co-editor (with V.F.R.Jones, C.Gordon, L.Kauffman and S.Lambropoulou), Proceedings of

International Conference “Knots in Hellas 98”, Volume 3, In: JKTR 10(5), August 2001, 170

pages.

(3) Co-editor (with V.F.R.Jones, C.Gordon, L.Kauffman and S.Lambropoulou), Proceedings of

International Conference “Knots in Hellas 98”, Volume 2. In: JKTR 10(2), March 2001, 175

pages.

(2) Co-editor (with V.F.R.Jones, C.Gordon, L.Kauffman and S.Lambropoulou), Proceedings of In-

ternational Conference “Knots in Hellas 98”, Volume 1. In the Series on Knots and Everything,

Vol. 24 , 2000, 600 pp.

(1) Co-editor (with V.F.R.Jones, J.Kania-Bartoszy´nska, V.Tuarev and P.Traczyk), Banach Center

Publications, Vol. 42, “Knot Theory”, 1998, 463 pages.

Reviewing and refereeing

Reviewer of Mathematical Reviews of AMS and of Zentralblatt f¨ur Mathematik - Mathematics Abstracts.

Referee of papers submitted to various journals including:

Inventiones Mat., Topology, Topology and its Applications, Trans. Amer. Math. Soc., Pacific

J.Math., Proc. Amer. Math. Soc., Math. Proc. Cambridge Philosophical Society, Canadian Math. Journal, Fundamenta Math., Journal of the Lond. Math. Soc., Bulletin of the London Mathematical Society, Journal of Knot Theory and its Ramifications, Annales Scientifiques de L’´Encole Normale Sup´erieure, Kobe Journal of Math., Asian Journal of Mathematics, Communications in Analysis and Geometry, Geometriae Dedicata, Revista Matematica, Quantum Information Processing, The International Journal of Sciences, Journal of Algebraic and Geometric Topology, l’Enseignement Mathematique, GT (Geometry and Topology; Warwick UK), AGT (Algebraic and Geometric Topology; Warwick UK), Bull. LMS, Advances in Mathematics.

Reviewer of NSF grant proposals. Participant in NSF panel on Topology, February 2006, NSF

(CBMS) panel June 2007.

Reviewer of NSA grant proposals.

Reviewer of proposals submitted to the CRDF Cooperative Grants Program.

Organizing Conferences

1. I am preparing organization of several International conferences in the future. In particular:

Knots in Poland III, Stefan Banach International Mathematical Center, Poland, July 19-25, Warsaw, and July 25- August 4, 2010, Bedlewo (with Joanna Kania-Bartoszynska and Pawel Traczyk).

2. Co-organizer (with M.Khovanov and R.Sazdanovic), the special session of AMS: Homology theories for knots and skein modules, ”Homology theories for knots and skein modules” at 2010 Spring Eastern Sectional Meeting May 22-23, 2010, New Jersey Institute of Technology, Newark (APPROVED).

3. Co-organizer (with Y.Rong, R.Sazdanovic, A.Schumakovitch, and H.Wu) of Knots in Washington XXIX, 30 years of Quandles, 10 years of Khovanov homology, December 4-6, 2009 (NSF supported).

4. Co-organizer (with S.Jablan, L. Kauffman, and S.Lambropoulou) of the Advanced School and Conference on Knot Theory and its Applications to Physics and Biology at the International Centre for Theoretical Physics, Trieste, Italy, May 11-29, 2009;

(http://cdsagenda5.ictp.trieste.it/full display.php?smr=0&ida=a08157)

5. Co-organizer (with M.Dabkowski, V.Ramakrishna, Y.Rong, A.Schumakovitch, K.Taniyama, and H.Wu) of Knots in Washington XXVIII (follow up to Workshop on Knots and quantum computing), GWU, February 27 – March 1, 2009 (NSF supported);

6. Co-organizer (with Oyama, Y.Rong, A.Schumakovitch, K.Taniyama, T.Tsukamoto, H.Wu, and A.Yasuhara) Knots in Washington XXVII, GWU, January 9-11, 2009 (NSF supported);

7. Co-organizer (with V. Harizanov), the special session of AMS: Orderings in Logic and Topology, January 4-8, 2009, to be held at Washington, DC.

8. Co-organizer (with K.Pawalowski, W.Rosicki, A.Szczepanski) Conference on Algebraic and Geometric Topology June 09-13, 2008, Gdansk, Poland.

9. Co-organizer (with L.Kauffman, S.King, V.Manturov), International Workshop “Invariants in Low Dimensional Topology” in Oberwolfach, Germany, May 4-10, 2008.

10. Co-organizer (with Y.Rong, A.Schumakovitch, and H.Wu) Knots in Washington XXVI, GWU, April 18-20, 2008 (NSF supported).

11. Co-organizer (with M.K.Dabkowski and V.Ramakrishna), Workshop on Knots and quantum computing, University of Texas at Dallas, December 16-22, 2007 (supported by an NSF grant).

12. Co-organizer (with Y.Rong, A.Schumakovitch, D.Silver, and H.Wu), conference Knots in Washington XXV, GWU, December 7-9, 2007.

13. Co-organizer (withM.K.D¸abkowski, A.S.Sikora and P.Traczyk), of the special session of AMS/PTM

International Meetings: “Invariants of links and 3-manifolds” Warsaw, Poland, July 31 – August 3, 2007.

14. Co-organizer (with Y.Rong and A.Schumakovitch) Knots in Washington XXIV; Dedicated to the memory of Xiao-Song Lin April 13-15, 2007, GWU.

15. Co-organizer (with J.Kania-Bartoszynska and P.Traczyk), Workshop: Knots and Braids, Banach Center, Warsaw, Poland, Dec. 11-17, 2006;

16. Co-organizer (with Y.Rong and A.Schumakovitch); Knots in Washington XXIII; Quandles, their homology and ramifications, November 17-19, 2006.

17. Co-organizer (with Y.Rong and A.Schumakovitch) Knots in Washington XXII, GWU, May 5-7, 2006.

18. Co-organizer (with Y.Rong and A.Schumakovitch) Knots in Washington XXI: Skein modules, Khovanov homology and Hochschild homology, GWU, December 9-11, 2005.

19. Co-organizer (with Louis H. Kauffman and Fernando J. O. Souza) AMS-IMS-SIAM Joint Summer Research Conference; Quantum Topology–Contemporary Issues and Perspectives, Snowbird Resort, Snowbird, Utah, Sunday, June 5 – Thursday, June 9, 2005,

20. Co-organizer (with M.D¸abkowski and R.Gelca), the special session of AMS: “Invariants of links

and 3-manifolds” at the AMS Meeting in Lubbock (Meeting #1006), April 8-10, 2005.

21. Co-organizer (with S.Lambropoulou, Y.Rong) Knots in Washington XX; 60th birthday of Louis

H. Kauffman, GWU, February 11-13, 2005.

22. Co-organizer (with P.Kainen, Y.Rong) Knots in Washington XIX: Topology in Biology 2, Georgetown University and GWU, November 12-14, 2004.

23. Co-organizer (with Marta M.Asaeda and Adam S.Sikora) the special session of AMS: “Invariants of knots and 3-manifolds” at the AMS meeting in Pittsburgh (Meeting #1002), November 6-7, 2004).

24. Co-organizer (with Y.Rong ) Knots in Washington XVIII: Khovanov homology, GWU, May28-30, 2004.

25. Co-organizer (with M.M.Asaeda, M.K.D¸abkowski, Y.Rong) Knots in Washington XVII, December 19-21, 2003, GWU.

26. Co-organizer (with Joanna Kania-Bartoszy´nska, Pawel Traczyk, Vladimir Turaev and Bronek Wajnryb) of the international conference/mini-semester: “Knots in Poland 2003”, July 7-13,

2003 (Warsaw), July 14-27, 2003, Bedlewo.

27. Co-organizer (with M.Asaeda, W.Goldman and J.Millson) Knots in Washington XVI, May 5-7, 2003, UMD.

28. Co-organizing (with Mark Kidwell and Yongwu Rong ) the special session of AMS: “Algebraic Topology Based on Knots at the January 2003 AMS meeting in Baltimore, MD.

29. Co-organizer (with K.Kobayashi, Y.Rong, S.Suzuki, K.Taniyama, T.Tsukamoto and A.Yasuhara), Knots in Washington XV (Japan-USA Workshop on Knot Theory II); January 10-15, 2003, GWU and JHU.

30. Co-organizer (with Dubravko Ivansic and Yongwu Rong) Knots in Washington XIV, GWU, May 17, 2002

31. Co-organizer (with Dubravko Ivansic) of the conference Knots in Washington, XIII, December

16, 2001 (see: http://gwis2.circ.gwu.edu/ przytyck/knots/index.html)

32. Co-organizing (with L.Kauffman and F. Souza) the special session of AMS: “Quantum Topology”. November 10-11, 2001 Irvine, CA (2001 Fall Western Section Meeting) Meeting # 972.

33. Co-organizer (with Dubravko Ivansic, Ilya Kofman, Yongwu Rong and Akira Yasuhara) of the conference Knots in Washington, XII, May 10-12, 2001

(see: http://home.gwu.edu/ przytyck/knots/index.html)

34. Co-organizer (with Dubravko Ivansic, Yongwu Rong, Dan Silver and Akira Yasuhara) of the

conference Knots in Washington, XI, December, 2000.

35. Co-organizer (with Kazuaki Kobayashi, Yongwu Rong, Kouki Taniyama, Tatsuya Tsukamoto

and Akira Yasuhara) of the conference Knots in Washington, X, Japan - USA ; workshop in

Knot Theory, (GWU and UMCP) January 23-30, 2000

36. Co-organizer (with D.Ivansic, Y.Rong, and T.Stanford) of the special session of AMS: “Invari-

ants of Knots and 3-manifolds” at the January 2000 AMS meeting in Washington, D.C.

37. Co-organizer (with Y.Rong) of Knots in Washington, IX, Conference on Knot Theory and its

Ramifications, September 24-25 , 1999, at the George Washington University.

38. Co-organizer (with Y.Rong) of the conference on Knot Theory and its Ramifications: “Knots

in Washington”, VIII, GWU, April 30 – May 1, 1999.

39. Co-organizer (with S.Naik) of the special session of AMS: Symmetries of Knots and Three- manifolds; 1999 Spring Western Section Meeting Las Vegas, NV, April 10-11, 1999 Meeting #942

40. Co-organizing (with P.Kainen and Y.Rong) a conference on Knot Theory and its Ramifications: “Knots inWashington, VII (Topology in Biology), Georgetown University, October 23-24, 1998

41. Co-organizing with C.Gordon, V.F.R.Jones, S.Lambropoulou,S.Negrepontis Knots in Hellas – International Conference on Knot Theory and its ramifications, Delphi (Greece) August 7-15, 1998;

42. Co-organizing a conference on Knot Theory and its Ramifications: Knots Theory days - Knots in Washington, VI; Feb.8-9, 1998, U.S. Naval Academy, Annapolis.

43. Co-organizing the special session of AMS: Knot Theory and Quantum Topology. (at American Mathematical Society Meeting in Baltimore), Jan. 9-10, 1998.

44. Co-organizing a conference on Knot Theory and its Ramifications: “Knots in Washington, V”, University of Maryland (College Park), November 22, 1997.

45. Co-organizing the special session of AMS: Knot Theory and 3-Manifolds, University of Maryland, College Park, April 12-13, 1997.

46. Co-organizing a conference on Knot Theory and its Ramifications: “Knots in Washington IV”(it is one in the series of conferences devoted to knot theory and its ramifications), University of Virginia, April 5, 1997.

47. Co-organizing a conference on Knot Theory and its Ramifications: “Knots in Washington; III”,GWU, October 18-20, 1996.

48. Co-organizing a mini-conference on Knot Theory and its Ramifications: “Knots in Washington; II”, GWU, March 30, 1996.

49. Co-organizing a mini-conference on Knot Theory and its Ramifications: “Knots in Washington; I”, GWU, October 28, 1995.

50. Co-organizing (with V.F.R. Jones, J. Kania-Bartoszy´nska, P. Traczyk and V.G. Turaev) a mini-semester on Knot Theory at the Stefan Banach International Mathematical Center (Warsaw, Poland), July 17, 1995—August 18, 1995.

51. Directed the Spring Mathematical School on Differential Topology for talented undergraduate students, 1979.

52. Member of Scientific Committee of Low Dimensional Topology Conference organized in January 1998 at Universidade da Madeira (Portugal).

53. Member of the International Advisory Board of the First International Workshop on Graphs– Operads – Logic, Cuautitl´an, M´exico, March 12-16, 2001.

54. Member of the International Advisory Board of the Third International Workshop on Graphs– Operads – Logic, M´exico, February 4-13, 2004.

National Science Foundation (NSF) and NSA support(1) NSF-DMS-9808955, July 15, 1999 – June 30, 2000. Amount awarded: $ 34,000.

(2) NSF (AN: CCLS20221A) May 1, 2004 - April 30, 2005

Amount awarded: $10,000.

Project Title: Knots in Washington XVIII; Khovanov homology

(3) PI in the NSF proposal DMS-0555648, January 1, 2006 – December 31, 2006

Amount awarded: $20,000.

Project Title: Knots in Washington XXI: Skein modules, Khovanov homology and Hochschild homology

(4) Co-PI in NSF grant (# 0745204) ”Workshop on Knots and Quantum Computing” (M.Dabkowski from UT Dallas is the PI); Total Award Period Covered: September 1, 2007 - August 31, 2008; it was extended till August 2009;

Total Award Amount: $24,000; grant to organize interdisciplinary conference.

(5) PI in the National Security Agency (NSA) Project ”Quandles, Burnside Groups, Skein Modules and Khovanov Homology: Investigating Algebraic Structures Motivated by Knot Theory”,

Total Award Amount: $61,548,; personal research grant

Grant was awarded for the period March 21, 2008 - March 21, 2010.

Total Award Amount: $61,548

(6) PI in NSF grant Proposal for ”Knots in Washington” conferences, for 3-years starting March of 2008 (Y.Rong, A.Shumakovitch and H.Wu are co-PI).

Total Award Amount: $ 97,971.00; grant to organize Knots in Washington conferences.

Grant was awarded for the period May 15, 2008 - April 30, 2011.

(7) Co-PI in the Polish Scientific Grant: Nr. N N201387034; Grant was awarded for the period April 29, 2008 – April 29, 2011.

(I am one of many participant - the only one from outside of Poland - the grant should allow us to invite Polish mathematicians to GWU or/and finance my trip to Poland to deliver series of lectures).

(8) Co-PI in the NSF grant (DMS- 0925541) (PI. L.Kauffman).

$ 28,000 Total Award Period Covered: 03/01/09 - 02/28/10

ICTP Summer School and Conference on Knot Theory.

Approved, April 9, 2009

Other grants outside GWU(1) Co-PI in the Polish Scientific Grant: Nr. N N201387034; Grant was awarded for the period

April 29, 2008 – April 29, 2011.

(I am one of many participant - the only one from outside of Poland - the grant should allow

us to invite Polish mathematicians to GWU or/and finance my trip to Poland to deliver series

of lectures).

(2) Co-PI-director (with S.Jablan, L.Kauffman and S.Lambropoulou) of the grant to organize ICTP

Summer School and Conference on Knot Theory, Trieste, Italy (11-29 May 2009). It is awarded

by European Union grant agency via ICTP. Amount: 50,000 Euro (appr. $75,000) Grant was

covering expenses of third world participants of the School and Conference at European Union

grant via ICTP (International Centre for Theoretical Physics, Trieste, Italy), and to cover costs

of publishing Proceedings of the School and Conference.

Teaching Experience:

1. Taught courses in topology of 3-manifolds, knot theory, linear and abstract algebra, analytical functions and differential geometry (at Warsaw University before 1995), Topologia niskowymi-arowa i Teoria w¸ez l´ow (Knot theory and low-dimensional topology) (Warsaw University, 2000). Taught also a graduate course in algebraic topology at UBC (1986-1987), a course in calculus at University of Toronto (1987-1988), a course in linear algebra (UBC Spring 1989), “Geometry of graphs and knots” (UBC summer 1989), a graduate course “Skein invariants of links in 3-manifolds, Yang-Baxter equation and statistical mechanics” (Michigan State Univ., Fall 1989), a course “An introduction to the theory of numbers” (UBC, Summer 1990), two courses in calculus (UC Riverside), and courses in Knot Theory, Convex Analysis, and Representations of Groups and Algebras (Odense University).

Teaching at GWU:

- Fall semester 2009:

Math. 9-11 (Mathematical ideas I); Enrollment 70

Math 801: The Dean’s Seminar: Geometry of Knots and Graphs: a historical perspective, Enrollment (5).

Math. 195: Undergraduate Independent study (3 students);

- Spring semester 2009:

Math. 10-10 (Mathematical ideas II); Enrollment 70

Math 282 (Algebraic Topology); Enrollment 12.

Math. 295: Reading and Research for Radmila Sazdanovic

- Fall semester 2008:

Math. 9-13 (Mathematical ideas I); Enrollment 70

Math 281 (General and Geometric Topology); Enrollment 8.

Math. 295: Reading and Research for Radmila Sazdanovic.

Math. 195: Undergraduate Independent study;

- Spring semester 2008:

Math 801: The Dean’s Seminar: Geometry of Knots and Graphs: a historical perspective, Enrollment (19).

- Math. 286: Knot Theory and Low Dimensional Topology II, Enrollment (3+2)

- Reading and Research (295),

- Fall semester 2007:

Reading and Research (295),

Math. 9-13 (Mathematical ideas I); Enrollment 70

Math. 285 (Knot Theory and Low Dimensional Topology), Enrollment 5.

- Spring semester 2007:

Reading and Research (295) (with M.Pabiniak and R.Sazdanovic).

- Fall semester 2006:

Reading and Research (295) (two courses):

(i) Categorification of state sums; can Khovanov homology detect phase transition?

(ii) Skein modules

- Spring semester 2006:

The Dean’s Seminar: Geometry of Knots and Graphs: a historical perspective; Enrollment 9.

Math. 289 (Topics in Algebra: Skein modules, Khovanov homology and Hochschild homology); Enrollment 3

Reading and Research (295), Chromatic homology for graphs as homology of cell complexes; (for M.Pabiniak, R.Sazdanovic), NEW COURSE

Reading and Research (295), Commutative Kei (for M.Niebrzydowski), NEW COURSE

- Fall semester 2005:

Math. 9-13 (Mathematical ideas I); Enrollment 69.

Math. 9-14 (Mathematical ideas I); Enrollment 71.

Reading and Research (295), Introduction to Homological algebra (for M.Niebrzydowski, M.Pabiniak, R.Sazdanovic), NEW COURSE

Reading and Research (295), Homology of groups (for M.Niebrzydowski), NEW COURSE

- Spring semester 2005:

Math. 282 (Algebraic Topology); Enrollment (about 4)

Reading and Research (295) for M.Niebrzydowski.

- Fall semester 2004:

Math. 9 (Mathematical ideas I); Enrollment 77.

Math. 281 (General Topology); Enrollment 12.

Reading and Research (295), Quandles (for F.Jasso-Hernandez, M.Niebrzydowski)

- Spring semester 2004:

Reading and Research (295), (for G.Barad, F.Jasso-Hernandez, M.Niebrzydowski)

- Fall semester 2003:

The Dean’s Seminar: Geometry of Knots and Graphs: a historical perspective, NEWCOURSE

- Reading and Research (295), ”Temperley-Lieb algebras” (for G.Barad). NEW COURSE

- Reading and Research (295), ”Burnside groups” (for G.Barad, F.Jasso-Hernandez). NEW COURSE

- Spring semester 2003:

Math. 10 (Mathematical ideas II); Enrollment 85

- Fall semester 2002:

Math. 9 (Mathematical ideas I); Enrollment 72.

Math. 289 (Topics in Topology - “Rotors, Lagrangians and skein modules of Knots”

Enrollment 4 (plus 5 other researchers), NEW COURSE

Dissertation Research (399) (for M.D¸abkowski, M.Veve)

- Spring semester 2002:

Math. 10 (Mathematical ideas II); Enrollment 73

Math. 289 (Topics in Topology - ”Skein algebras, character varieties and group orderings”

Enrollment 3 (plus 4 other researchers), NEW COURSE

Dissertation Research (399) (for M.Dabkowski)

- Fall semester 2001:

Math. 9 (Mathematical ideas I); Enrollment 72.

Dissertation Research (399) (for M.Dabkowski)

- Spring semester 2001:

Math. 10 (Mathematical ideas II); Enrollment 50

Math. 398: Advanced Reading and Research/Topics in Topology: Knotting of ideas from algebra geometry and topology; Enrollment 3 (plus 3 research visitors), NEW COURSE

Math. 398: Advanced Reading and Research (for M.Dabkowski)

(i) Noncommutative torus in Knot Theory

(ii) Symplectic structure in knot theory

Dissertation Research (399) (for M.Veve).

- Fall semester 2000:

Math. 9 (Mathematical ideas I); Enrollment 77.

Math. 289 (Topics in Topology; From lattice knots through symplectic colorings to skein

algebras); Enrollment 3. NEW COURSE

Math. 398: Advanced Reading and Research (M.Dabkowski) Character Varieties and skein modules.

Dissertation Research (399) (for M.Veve).

- Summer semester 2000:

Math. 10 (Mathematical ideas II); Enrollment 17.

Math. 3 (College Algebra); Enrollment 6.

- Spring semester 1999:

Math. 10 (Mathematical ideas II); Enrollment 57.

Math. 289 (Topics in Topology - Topics in Algebra Situs). Enrollment 6. NEW COURSE

Advanced Reading and Research (398) Topics in skein modules (forM.Sokolov, T.Tsukamoto, and M.Veve).

Math. 195 ( Reading and Research) A group of Coxeter and 3-moves; (for Qi Chen).

- Fall semester 1998. Math 31 Single Variable Calculus I; Enrollment 70.

Math. 138 Advanced Calculus I; Enrollment 8.

Advanced Reading and Research (398) Topics in skein modules (forM.Sokolov, T.Tsukamoto, and M.Veve).

- Spring semester 1998:

Math. 10 (Mathematical ideas II); Enrollment 75.

Math. 195 ( Reading and Research), Simony knots and continued fractions, (for E.Grgeta).

Math. 295 (Topics in Topology - Skein modules of manifolds). Enrollment 5. NEW COURSE

Advanced Reading and Research (398), Moves on links and related filtered skein modules (for T.Tsukamoto).

Advanced Reading and Research (398), Young symmetrizers and their topological quantizations. (for M.Sokolov).

Dissertation Research (399), Structure of 3-manifold invariants coming from local skein relations. (for M.Sokolov).

- Fall semester 1997.

Math 33 (Multi-Variable Calculus). Enrollment 39.

Math 106; Introduction to Topology (advanced undergraduate course) Enrollment 3.

Reading and Research (295), ”A formal inverse to the Cayley– Hamilton theorem”, (for A.Raischi).

Advanced Reading and Research (398), ”Topological Quantum Field Theories (TQFT) from 3-manifold invariants” (for M.Sokolov).

- Spring semester 1997.

Math 32 (Calculus 2). Enrollment 28.

Math. 181: The advanced undergraduate course “Research Seminar”. (Scientific applications of Knot Theory. Applications to Biology, Chemistry and Physics.) Enrollment 4. NEW COURSE

Reading and Research (295) “The second skein module of 3-manifolds”. (for M.Sokolov).

- Fall semester 1996.

Math 31 (Calculus 1). Enrollment 82.

Math. 289. The graduate course: Topics in Topology - “Algebraic Topology based on Knots. Introduction”, Enrollment 6. NEW COURSE

Reading and Research (295):“Skein algebras and character varieties”. (for A.Sikora and M.Sokolov).

- Spring semester 1996.

Math 31 (Calculus 1). Enrollment 67.

Math. 282. The graduate course “Algebraic Topology”. Enrollment 9.

Reading and Research (295) “Skein module approach to Reshetikhin-Turaev-Witten and Vassiliev-Gusarov invariants” (for M.McDaniel and A.Sikora).

Advanced Reading and Research (398) “Skein algebras of groups and skein modules of links” (for A.Sikora).

- Fall semester 1995.

Math. 32 (Calculus 2). Enrollment 42. Math. 281; The graduate course “General Topology”. Enrollment 9.

Reading and Research (295) “Skein algebras and Topological Quantum Field Theories (for A.Sikora).

2. Five publications in educational journals (see the list of publications).

Nominations1. Nominated for King Faisal International Prize in Mathematics, 2005.

2. Nominated for the Prize for Excellence in Academic Advising in CSAS for 1999.

3. Nominated for the Trachtenberg Prize for Teaching for 1998.

4. Nominated for a prize for Excellence in Academic Advising in Columbian School School of Art and Sciences; May 1997.

Theses supervised:

Graduate level:

Joanna Kania-Bartoszy´nska, (MA, Warsaw University, 1982),

Anna Brzezi´nska, (MA, Warsaw University, 1985),

Lech Ka´zmierczak, (MA, Warsaw University, 1983),

Jan Olszewski, (MA, Warsaw University, 1986);

Adam S. Sikora (MA, GWU 1997),

Qi Chen (MA, GWU 1999) Thesis: “The 3-move conjecture for 5-braids”.

Tatsuya Tsukamoto (PhD, May 2000, GWU),

Thesis: ”The fourth Skein module for 4-algebraic links”.

Maxim Sokolov (PhD, May 2000, George Washington University),

Thesis: “Quantum Invariants, Skein Modules, and Periodicity of 3-Manifolds”.

Mieczys law D¸abkowski (PhD, May 2003, GWU),

Thesis: “Third Skein Modules of links and Burnside groups”.

Mike Veve (PhD, July 2006, George Washington University,

defense, July 31, 2006; Thesis: “Skein modules, Orderable Magmas and Billiard knots”),

Maciej Niebrzydowski (PhD, April 2007, George Washington University).

defense April 30, 2007; Thesis: “Some applications of quandles and their homology to the geometry

of knots”.

Milena Pabiniak (MA, George Washington University, 2008).

Radmila Sazdanovic (PhD, planned Jan 2010, George Washington University).

Undergraduate level:

Edi Grgeta (GWU, 1998), senior thesis (special honors project).

Thesis: Simony knots and continued fractions.

LIST OF PUBLICATIONS

J´ozef H. Przytycki

Books

1. Topology of 3-dimensional manifolds, (with W.Jakobsche), Warsaw University Press, (1987), in Polish.

2. Knots: a combinatorial approach to knot theory, Script, Warsaw, August 1995, 240+ XLVII- Ipp., (in Polish, English translation (extended) in preparation; to be published by Cambridge University Press).

3. 14 volumes for which I was an editor (see Editing).

Books in preparation

1. KNOTS: From combinatorics of knot diagrams to the combinatorial topology based on knots,

Cambridge University Press, accepted for publication, to appear 2010, pp. 600.

Chapter II, e-print: http://arxiv.org/abs/math/0703096

Chapter V, e-print: http://arxiv.org/abs/math.GT/0601227

Chapter IX, e-print: http://arxiv.org/abs/math.GT/0602264

Chapter X, e-print: http://arxiv.org/abs/math.GT/0512630

2. Algebraic topology based on knots, Series on Knots and Everything - Vol. 18, World Scientific,

in preparation.

3. Topology of 3-dimensional manifolds, (with W.Jakobsche), Second edition, accepted for publi-

cation, Script, Warsaw, 2010. (in Polish)

4. Translation of the above book into Ukrainian, in preparation.

Papers published or accepted for publication

1. Some remarks on actions of Zn-groups on 3-manifolds, Bull. Ac. Pol. Scie. Ser. Math. Astr. Phys XXVI (7) 1978, 625 - 633.

2. Free actions of Zn on handlebodies and surfaces, Bull. Ac. Pol. Scie. Ser. Math. Astr. Phys., XXVI (7)1978, 617-624.

3. A unique decomposition theorem for 3-manifolds with boundary, Bull. Ac. Pol.: Math., XXVII (2) 1979, 209-215.

4. Zn-actions on some 2- and 3-manifolds, Geometric Topology, Proc. Int. Conf. Warszawa 1978, 353-359 (1980).

5. Zn actions on 3-manifolds, Colloq. Math. 47, 1982,199-219.

6. Actions of Zn on some surface-bundles over S1, Colloq. Math. 47, 1982, 221-239.

7. Cyclic actions on S2 and P2-bundles over S1, Colloq. Math. 47, 1982, 241-254.

8. Incompressibility of surfaces after Dehn surgery, Michigan Math. J. 30, 1983, 289-308.

9. Nonorientable,incompressible surfaces of genus 3 inM ( /μ) manifolds, Collectanea Math XXXIV(1), 1983 ,37-79.

10. Incompressibility of surfaces with four boundary components after Dehn surgery, Demonstratio Math. XVII (1), 1984, 119-126.

11. Incompressible surfaces in the exterior of a closed 3 braid. I. Surfaces with horizontal boundary components (with M.Lozano), Math. Proc. Cambridge Phil. Soc., 98, 1985, 275-299.

12. n-relator 3-manifolds with incompressible boundary, in: Low-dimensional topology and Kleinian groups, edited by D.B.A. Epstein, London Math. Soc. LNS 112 ,1986, 273-285.

13. Hyperbolic structures on Dehn fillings of some punctured-torus bundles over S1 (with S.Betley and T.˙Zukowski), Kobe J. Math., 3(2), 1986, 117-147.

14. Invariants of links of Conway type (with P.Traczyk), Kobe J.Math., 4, 1987, 115-139.

15. Conway algebras and skein equivalence of links (with P.Traczyk), Proc. Amer. Math. Soc., 100(4), 1987, 744-748.

16. tk moves on links, Contemporary Math. Vol. 78, Braids - Proceedings of the Santa Cruz conference on Artin’s braid groups (July 1986), 1988, 615-656;

e-print: http://arxiv.org/abs/math.GT/0606633

17. Plans’ theorem for links: An application of tk moves, Canad. Math. Bull. 31(3), 1988, 325-327.

18. tk-equivalence of links and Conway formulas for the Jones-Conway and Kauffman polynomials, Bull. Polish Acad. Sci. Math., 36(11-12), 1988, 675-680.

19. On spines of knots spaces (with W.J.R.Mitchell and D.Repovs), Bull. Ac. Pol.: Math., 37, 1989, 563 - 566.

20. Knot polynomials and generalized mutation (with R.P.Anstee and D.Rolfsen) Topology and its appl., 32, 1989, 237-249.

e-print: http://front.math.ucdavis.edu/math.GT/0405382

21. An invariant of dichromatic links (with J.Hoste), Proc. Amer. Math. Soc., 105(4), 1989, 1003-1007.

22. On Murasugi’s and Traczyk’s criteria for periodic links, Math. Ann., 283, 1989, 465 - 478.

23. Equivalence of cables of mutants of knots, Canadian Journal Math., XLI(2), 1989, 250-273.

24. The Skein polynomial of a planar star product of two links (with K.Murasugi), Math. Proc. Cambridge Phil. Soc., 106, 1989, 273-276.

25. Positive knots have negative signature, Bull. Ac. Pol.: Math. 37, 1989, 559-562.

26. On lower bound for short noncontractible cycles in embedded graphs (with T.Przytycka), SIAM J. Discr. Math. 3(2), 1990, 281-293.

27. t3, t4 moves conjecture for oriented links with matched diagrams, Math. Proc. Cambridge Phil. Soc., 108, 1990, 55-61.

28. Homotopy skein modules of oriented 3-manifolds (with J.Hoste), Math. Proc. Cambridge Phil. Soc., 1990, 108, 475-488.

29. Skein modules of 3-manifolds, Bull. Ac. Pol.: Math.; 39(1-2), 1991, 91-100;

e-print: http://arxiv.org/abs/math/0611797

30. A survey of skein modules of 3-manifolds (with J.Hoste); in Knots 90, Proceedings of the International Conference on Knot Theory and Related Topics, Osaka (Japan), August 15-19,

1990), Editor A. Kawauchi,Walter de Gruyter 1992, 363-379.

31. Skein module of links in a handlebody, Topology 90, Proc. of the Research Semester in Low Dimensional Topology at OSU, Editors: B.Apanasov, W.D.Neumann, A.W.Reid, L.Siebenmann, De Gruyter Verlag, 1992; 315-342.

32. Quantum group of links in a handlebody Contemporary Math: Deformation Theory and Quantum Groups with Applications to Mathematical Physics, M.Gerstenhaber and J.D.Stasheff, Editors, Volume 134, 1992, 235-245.

33. Surface triangulations with long noncontractible cycles, (with T.Przytycka); Contemporary Mathematics, 147: Graph Structure Theory, 1993, 303-340.

34. Subexponentially computable truncations of Jones-type polynomials, (with T.Przytycka), in “Graph Structure Theory”, Contemporary Mathematics 147, 1993, 63-108.

35. Elementary conjectures in classical knot theory, in Quantum Topology, Ed. L.J.Kauffman, R.A.Baadhio, Series on Knots and Everything - Vol.3, World Scientific, 1993, 292-320.

36. The (2,∞)-skein module of lens spaces; a generalization of the Jones polynomial (with J. Hoste), Journal of Knot Theory and Its Ramifications, 2(3), 1993, 321-333.

37. An index of a graph with applications to knot theory (with K.Murasugi); Memoirs of the American Math. Soc., Vol. 106, Number 508, November 1993, 101 pages.

38. Vassiliev-Gusarov skein modules of 3-manifolds and criteria for periodicity of knots, Low- Dimensional Topology, Knoxville, 1992 ed.: Klaus Johannson International Press Co., Cambridge, MA 02238, 1994, 143-162.

39. A note on the Lickorish-Millett-Turaev formula for the Kauffman polynomial, Proc. Amer. Math. Soc., 121(2), 1994, 645-647.

40. The skein module of genus 1 Whitehead type manifolds (with J.Hoste), Journal of Knot Theory and Its Ramifications, 4(3), 1995, 411-427.

41. The Kauffman bracket skein module of S1 × S2 (with J.Hoste), Math. Z., 220(1), 1995, 63-73.

42. Search for different links with the same Jones’ type polynomials: Ideas from graph theory and statistical mechanics, Panoramas of Mathematics, Banach Center Publications, Vol. 34,

Warszawa 1995, 121-148. e-print: http://front.math.ucdavis.edu/math.GT/0405447

43. An elementary proof of the Traczyk-Yokota criteria for periodic knots, Proc. Amer. Math. Soc., 123, 1995, 1607–1611.

44. A simple construction of high representativity triangulations, (with T.Przytycka); Discrete Mathematics, 173, 1997, 209-228.

45. Index of graphs and non-amphicheirality of alternating knots (with K.Murasugi), Progress in knot theory and related topics, Travaux en Cours, 56, Hermann, Paris, 1997; 20-28.

46. Algebraic topology based on knots: an introduction, Knots 96, Proceedings of the Fifth International Research Institute of MSJ, edited by Shin’ichi Suzuki, World Scientific Publishing Co., 1997, 279-297.

47. Tangle surgeries which preserve Jones-type polynomials (with J.Hoste), International Journal of Mathematics, 8, 1997, 1015–1027.

48. A q-analogue of the first homology group of a 3-manifold, Contemporary Mathematics 214, Perspectives on Quantization (Proceedings of the joint AMS-IMS-SIAM conference on Quantization, Mount Holyoke College, 1996); Ed. L.A.Coburn, M.A.Rieffel, AMS 1998, 135-144.

49. 3-coloring and other elementary invariants of knots, Banach Center Publications, Vol. 42, Knot Theory, 1998, 275-295;

e-print: http://arxiv.org/abs/math.GT/0608172

50. Skein algebra of a group (with A.S.Sikora), Banach Center Publications, Vol. 42, Knot Theory, 1998, 297-306.

51. Lissajous knots and billiard knots (with V.F.R.Jones), Banach Center Publications, Vol. 42, Knot Theory, 1998, 145-163.

52. Symmetric knots and billiard knots, Chapter 20 of the book Ideal Knots, Vol. 19 in Series on Knots and Everything, Ed. A.Stasiak, V.Katrich, L.Kauffman, World Scientific, 1999, 374-414.

e-print: http://front.math.ucdavis.edu/math.GT/0405151

53. Fundamentals of Kauffman bracket skein modules, Kobe Math. J., 16(1), 1999, 45-66.

e-print: http://front.math.ucdavis.edu/math.GT/9809113

54. Multiplicative structure of Kauffman bracket skein module quantizations (with D. Bullock), Proc. Amer. Math. Soc., 128(3), 2000, 923–931.

e-print: http://front.math.ucdavis.edu/math.QA/9902117

55. On Skein Algebras and Sl2(C)-Character Varieties, (with A.S.Sikora), Topology, 39(1), 2000, 115-148;

e-print: http://front.math.ucdavis.edu/q-alg/9705011

56. Estimating the Size of Skein Homologies (with J.Kania-Bartoszy´nska and A.S.Sikora), Knots in Hellas’ 98; The Proceedings of the International Conference on Knot Theory and its Ramifications; Volume 1. In the Series on Knots and Everything, Vol. 24, September 2000, pp. 138-142.

57. The Kauffman bracket skein module of a connected sum of 3-manifolds, Manuscripta Math., 101(2), 2000, 199–207;

e-print: http://front.math.ucdavis.edu/9911.5120

58. Polygon dissections and Euler, Fuss, Kirkman and Cayley numbers (with A.S.Sikora), Journal of Combinatorial Theory - series A, 92, 2000, 68-76;

e-print: http://arxiv.org/abs/math.CO/9811086

59. Homotopy and q-homotopy skein modules of 3-manifolds: an example in Algebra Situs; In: Knots, Braids, and Mapping Class Groups: Papers dedicated to Professor Joan Birman, Ed. J. Gilman, W. Menasco, and X.-S. Lin, International Press., AMS/IP Series on Advanced Mathematics, Vol 24, Co., Cambridge, MA, 2001, 143-170.

e-print: http://front.math.ucdavis.edu/math.GT/0402304

60. Kanenobu-Miyazawa conjecture and the Vassiliev-Gusarov skein modules based on mixed crossings (with K.Taniyama), Proc. Amer. Math. Soc., 129(9), 2001, 2799-2802.

61. The fourth skein module and the Montesinos-Nakanishi conjecture for 3-algebraic links (with T.Tsukamoto), J. Knot Theory Ramifications, 10(7), 2001, 959–982;

e-print: http://front.math.ucdavis.edu/math.GT/0010282

62. Surgeries on periodic links and homology of periodic 3-manifolds (with M.Sokolov), Math. Proc. Cambridge Phil. Soc., 131(2) 2001, 295-307;

e-print: http://front.math.ucdavis.edu/0002.5231

63. Topological Insights from the Chinese Rings (with A.S.Sikora), Proc. Amer. Math. Soc., 130(3), 2002, 893–902;

e-print: math.GT/0007134

64. The topological interpretation of the core group of a surface in S4 (with W. Rosicki), Canad. Math. Bull., 45(1), 2002, pp. 131-137;

e-print: http://arxiv.org/abs/math.GT/0403475

65. Burnside obstructions to the Montesinos-Nakanishi 3-move conjecture, (with M.K. D¸abkowski), Geometry and Topology, 6, June, 2002, 355-360;

e-print: http://front.math.ucdavis.edu/math.GT/0205040

66. 3-manifold invariants and periodicity of homology spheres, (with P.Gilmer and J.Kania-Bartoszynska), Algebraic and Geometric Topology 2, 2002, 825-842;

e-print: http://xxx.lanl.gov/abs/math.GT/9807011

67. Skein module deformations of elementary moves on links; Geometry and Topology Monographs Volume 4: Invariants of knots and 3-manifolds (Kyoto 2001), 2002 (published November 2003), 313-335

http://www.maths.warwick.ac.uk/gt/GTMon4/paper21.abs.html

68. Skein modules; Section 4 in “Problems and invariants of knots and 3-manifolds”, Geometry and Topology Monographs Volume 4: Invariants of knots and 3-manifolds (Kyoto 2001), 2002 (published June 1, 2004), 73-82;

e-print: http://arxiv.org/abs/math.GT/0406190

69. Symmetry of links and classification of lens spaces (with A.Yasuhara), Geometriae Dedicata, April 2003, Volume 98, Issue 1, 57-61;

e-print: http://arxiv.org/abs/math.GT/0011119

70. SUn-quantum invariants for periodic links (with A.S.Sikora), the AMS volume on Diagrammatic Morphisms and Applications, Contemporary Mathematics, 318, 199-205, 2003.

71. Branched covers of tangles in three-balls (with M.Ishiwata and A.Yasuhara), Canad. Math. Bull., 46(3), 2003, 356–364

e-print: http://front.math.ucdavis.edu/0109.5046

72. Kauffman-Harary Conjecture holds for Montesinos knots, (with M.M.Asaeda and A.S.Sikora), J. Knot Theory Ramifications, 13(4), June, 2004, 467-477;

e-print: http://front.math.ucdavis.edu/math.GT/0305415

73. Linking numbers in rational homology 3-spheres, cyclic branched covers and infinite cyclic covers (with A.Yasuhara), Trans. Amer. Math. Soc., 356 (9), 2004, 3669-3685.

Published electronically (posted January 16, 2004) : http://www.ams.org/tran/0000-000-00/S0002- 9947-04-03423-3/home.html

e-print: http://front.math.ucdavis.edu/math.GT/0111203

74. From 3-moves to Lagrangian tangles and cubic skein modules, Advances in Topological Quantum Field Theory, Proceedings of the NATO ARW on New Techniques in Topological Quantum Field Theory, Kananaskis Village, Canada from 22 to 26 August 2001; John M. Bryden (ed), October 2004, 71-125;

e-print: http://front.math.ucdavis.edu/math.GT/0405248

75. Categorification of the Kauffman bracket skein module of I-bundles over surfaces, (with M.M.Asaeda and A.S.Sikora), Algebraic & Geometric Topology (AGT), 4, 2004, 1177-1210;

e-print: http://front.math.ucdavis.edu/math.QA/0403527

76. Unexpected connection between Burnside groups and Knot Theory, (with M.K. D¸abkowski), Proc. Nat. Acad. Science, 101(50), December, 2004, 17357-17360;

e-print: http://front.math.ucdavis.edu/math.GT/0309140

77. Khovanov homology: torsion and thickness (with M.M.Asaeda), Advances in Topological Quantum Field Theory, Proceedings of the NATO ARW on New Techniques in Topological Quantum Field Theory, Kananaskis Village, Canada from 22 to 26 August 2001; J.M.Bryden (ed), 2004, 135-166

e-print: http://front.math.ucdavis.edu/math.GT/0402402

78. Rotation and signature invariants (with M. D¸abkowski, M.Ishiwata and A.Yasuhara), Fundamenta Mathematicae, 184, 79-97, 2004.

e-print: http://front.math.ucdavis.edu/math.GT/0407183

79. Non-left-orderable 3-manifold groups (with M.K.D¸abkowski and A.A.Togha), Canadian Math. Bull., 48(1), 2005; 32-40.

e-print: http://front.math.ucdavis.edu/math.GT/0302098

80. 3-manifolds, tangles and persistent invariants (with D.S.Silver and Susan G.Williams), Math. Proc. Cambridge Phil. Soc., 139, 2005, 291-306;

e-print: http://front.math.ucdavis.edu/math.GT/0405465

81. Torsion in Graph Homology (with L.Helme-Guizon and Y.Rong), Fundamenta Mathematicae, 190; June 2006, 139–177;

e-print: http://arxiv.org/abs/math.GT/0507245

82. Burnside Kei (with M.Niebrzydowski), Fundamenta Mathematicae, 190, 2006, 211–229;

e-print: http://front.math.ucdavis.edu/math.GT/0601004

83. A categorification of the skein module of tangles (with. M.M.Asaeda and A.S.Sikora), Contemporary Mathematics, 416: Primes and Knots, 2006, 1-8;

e-print: http://front.math.ucdavis.edu/math.QA/0410238

84. Compactness of the space of left orders (with M. A. Dabkowska, M. K. Dabkowski, V. S. Harizanov, M. A. Veve), Journal of Knot Theory and its Ram., 16(3), 2007, 257-266;

e-print: http://arxiv.org/abs/math.GT/0606264

85. 5-move equivalence classes of links and their algebraic invariants (with M.K.Dabkowski and M.Ishiwata), Journal of Knot Theory and its Ram., 16(10), December 2007; 1413–1449;

e-print: http://front.math.ucdavis.edu/0712.0985

86. The Gram matrix of the Temperley-Lieb algebra is similar to the matrix of chromatic joins (with Q.Chen), Communications in Contemporary Mathematics (CCM), 10, 2008, 849-855;

e-print: http://front.math.ucdavis.edu/0806.0878

87. Homology of dihedral quandles (with M.Niebrzydowski), Journal of Pure and Applied Algebra, 213, 2009, 742-755;

e-print: http://front.math.ucdavis.edu/math.GT/0611803

88. On the first group of the chromatic cohomology of graphs, (withM.D.Pabiniak and R.Sazdanovic), Geometriae Dedicata, 140(1), 2009, 19-48; Published online: November 12, 2008;

e-print: http://arxiv.org/abs/math.GT/0607326

89. The Quandle of the Trefoil as the Dehn Quandle of the Torus (with M.Niebrzydowski), Osaka Journal of Mathematics, 46 (3), 2009, 645-659;

e-print: http://front.math.ucdavis.edu/0805.2743.

90. The Gram determinant of the type B Temperley-Lieb algebra (with Q.Chen), Advances in Applied Mathematics, 43, 2009, pp. 156-161;

e-print: http://arxiv.org/abs/0802.1083

91. Nonorientable, incompressible surfaces in punctured-torus bundles over S1, Fundamenta Mathematicae, to appear.

92. Gram determinant of planar curves (with Xiaoqi Zhu); Involve, Accepted for publication

e-print: http://front.math.ucdavis.edu/0810.4649

93. From Goeritz matrices to quasi-alternating links; Heidelberg Knot Theory Semester Proceedings, accepted for publication, November 2009;

e-print: http://front.math.ucdavis.edu/0909.1118

94. When the theories meet: Khovanov homology as Hochschild homology of links, Quantum Topology, to appear;

e-print: http://arxiv.org/abs/math.GT/0509334

Preprints and Work in progress

1. Inductive construction of 2-connected graphs for calculating the virial coefficients (with E.Androulaki, S.Lambropoulou, I.G.Economou), submitted for publication, 2009;

e-print: http://front.math.ucdavis.edu/0907.4906

2. Almost positive links have negative signature (with K.Taniyama); preprint, 1991;

e-print: http://front.math.ucdavis.edu/0904.4130

3. Homology operations on homology of quandles (with M. Niebrzydowski);

e-print: http://front.math.ucdavis.edu/0907.4732

4. Gram determinant of curves on the Mobius band (with Q.Chen), in preparation.

5. Survey on recent invariants in classical knot theory, Warsaw University Preprints 6,8,9; 1986 (in English); a part of the book: Knots: combinatorial approach to the knot theory, 1995 (in Polish);

e-print: http://front.math.ucdavis.edu/0810.4191

6. Three talks in Cuautitlan under the general title: Topologia algebraica basada sobre nudos, Proceedings of the First International Workshop on ”Graphs – Operads – Logic, Cuautitlan, Mexico, March 12-16, 2001, to appear 2006 (in Spanish). Publiciationes Preliminares (Preprint) 717, Instituto de Matem´aticas Universidad Nacional Aut´onoma de M´exico, Fecha de reecibido: 7 de mayo de 2002; Presentado por Micho Durdevich.

e-print: http://front.math.ucdavis.edu/math.GT/0109029

7. Torsion in Khovanov homology of semi-adequate links (with R.Sazdanovic), in preparation.

8. Symplectic structure on Colorings, Lagrangian tangles and Tits buildings, (with J.Dymara and T.Januszkiewicz) preprint, May 2001.

9. Every link can be reduced by (2,2)- and ( 1 2)6-moves (with T.Tsukamoto), in preparation.

10. A non-commutative version of the Goeritz matrix of a link (with F.Jaeger), in preparation (preliminary version, August 1995).

11. Dichromatic modules of graphs, preprint 1993 (part of this paper is in Chapter V of my book:

e-print: http://arxiv.org/abs/math.GT/0601227).

12. Applications of Burnside groups in Knot theory, (with M. D¸abkowski), in preparation.

13. Homology of Takasaki quandles (with M. Niebrzydowski), in preparation.

14. The Homflypt and Kauffman skein modules of the product of the torus and the interval (with M. Mroczkowski), in preparation.

15. Incompressible surfaces in the exterior of a closed 3 braid. II.Surfaces with vertical boundary components (with M.Lozano); in preparation.

16. The spectral parameter 3-string tangle, in preparation.

17. Hecke algebra approach to skein modules of lens spaces (with S.Lambropoulou); in preparation.

18. Solution to Kauffman-Harary conjecture (withM.M.Asaeda, W.Menasco, A.S.Sikora), in preparation.

19. Skein algebras of surfaces, (with A.S.Sikora), in preparation.

20. Torsion in skein modules, in preparation.

Publications in Educational Journals

1. 3-rozmaito´sci wed lug Thurstona ( 3-manifolds according to Thurston), Delta, Warsaw, May 1984, 7-9, in Polish.

2. W¸ez ly i sploty (Knots and links), Delta, Warsaw, January 1985, 2-5, in Polish.

3. Knots and links, revisited, (with J.Kania-Bartoszy´nska) Delta, Warsaw, June 1985, 10-12, in Polish (expository article on generalizations of the Jones polynomial).

4. Podzia l `swi¸atecznej pomara´nczy (Division of a Christmas orange), Delta 9, September 1999, Warsaw, p.9-11; in Polish.

5. Podzia l czekolady (Division of a chocolate), Delta 4, April, 2000, Warsaw, p.8-9; in Polish.

6. Jak odr`o˙zni´c w¸ez lyi; in Polish (How to distinguish knots), Delta 4, April, 2002, p.8-9.

7. Czy co´s zosta lo dla nas? – 10 elementarych zaw¸e´zlonych problem´ow (Is there anything left for us? – 10 elementary knotted problems), Delta 5, May, 2002, p.V-VIII.

8. Kolorowanie splot´ow (Coloring of knots),Delta 7, July 2003, 8-10.

9. Knotaton – czyli wyscigi w¸ez l´ow (Knotathon – race of knots), preprint, 2000.

10. Hipoteza Montesinosa-Nakanishiego rozstrzygni¸eta po 20 latach, (Montesinose-Nakanishi conjecture solved after 20 years), in preparation.

Publications on History of Mathematics

1. History of the knot theory from Vandermonde to Jones, Aportaciones Matem´aticas Comunicaciones, 11 (1992), 173-185.

2. 200 years of knot theory, Wiadomo´sci Matematyczne, XXXI, 1995, 1-30; in Polish. Extended review in Math. Reviews: 98g:57001.

3. Classical roots of Knot Theory, Chaos, Solitons and Fractals, Vol. 9 (No. 4-5), 1998, 531-545.

4. The interrelation of the Development of Mathematical Topology in Japan, Poland and USA: Notes to the early history of the Knot theory in Japan, Annals of the Institute for

Comparative Studies of Culture, TWCU, Vol. 63, 2002, 61-86;

e-print: http://front.math.ucdavis.edu/math.HO/0108072

5. Dvisti rokiv teorii vuzliv (in Ukrainian), translation of the Polish article “Dwie´scie lat teorii w¸ez l´ow” (200 years of knot theory), preprint 2005.

6. Odrzucony medal Fieldsa: Grigorij Perelman i Hipoteza Poincare (in Polish) (Rejected Fields medal: Grigori Perelman and the Poincar´e Conjecture), preprint 2009.

Selected other professional publications, including Encyclopaedia of Mathematics entries(1999-2008

Invariants in low-dimensional topology. Abstracts from the workshop held May 4–10, 2008. Organized by Louis Kauffman, Simon King, Vassily Manturov and Jozef Przytycki. Oberwolfach Reports, 5(2), 2008,2007

A classification of links up to 5-move equivalence (with M.Dabkowski and M.Ishiwata); Proceeding of ”Topology of Knots X” conference at Tokyo Woman Christian University (TWCU), December 25, 2007, 7 pages (in Japanese).

2005

Rational moves and tangle embeddings: (2, 2)-moves as a case study (with Mieczys law K. D¸abkowski and Makiko Ishiwata), Proceedings of the Conference Topology of Knot VII (held at TWCU, December 23-26), February, 2005, 37-46, in Japanese;

e-print (in English): http://arxiv.org/abs/math.GT/0501539

(1999-2004)

1. q-homotopy skein module of 3-manifolds; properties and applications. Abstracts AMS, 20(3), 1999.

2. Homotopy quantization of skein modules. Abstracts AMS, 20(3), 1999.

3. The Kauffman bracket skein algebra of a surface times the interval has no zero divisors. Proceedings of the 46th Japan Topology Symposium at Hokkaido University (July 26–29, 1999), pp.52-61.

4. Little and Haseman – early American tabulators of knots. Abstracts AMS, 20(4), 1999.

5. The fourth skein module and Montesinos Nakanishi-Conjecture for 3-algebraic links (with T.Tsukamoto), Proceedings of the Conference “Topology of Knots”, TWCU, Tokyo, February, 2000, p. 55-59.

6. Are the Reshetikhin-Turaev-Whitten invariants determining the holonomy map of a hyperbolic 3-manifold? Abstracts AMS, 21(2), 2000.

7. Articles for Encyclopaedia of Mathematics, Supplement II. Ed. M.Hazewinkel; Kluwer Academic Publishers, 2000:

(i) Algebra Situs, p. 24.

(ii) Algebraic Topology Based on Knots, p.26.

(iii) Kauffman polynomial, pp. 289-290.

8. Symplectic structure on Colorings and Lagrangian tangles, Abstracts AMS, 21(4), December, 2000, p.545.

9. Symplectic structure on colorings of tangles, Abstracts AMS, 21(4), December, 2000, p.588.

10. Problem 10846, The American Mathematical Monthly, 108(1), January 2001, p.77, (solutions in 109(1), 2002, 79-80).

11. Symplectic form on t-colorings of tangles. Abstracts AMS, 22(2), 2001, p. 383.

12. Lagrangian approximation of Fox p-colorings of tangles; Fox approximation of rational pq -moves, Abstracts AMS, 22(3), 2001.

13. Encyclopaedia of Mathematics, Supplement III. Ed. M.Hazewinkel; Kluwer Academic Publishers, 2002; 25 articles; in particular:

(i) Alexander-Conway polynomial, p.29.

(ii) Alexander theorem on braids, p.29.

(iii) Brandt-Lickorish-Millett-Ho polynomial, p.82.

(iv) Conway algebra, pp.112-113.

(v) Conway skein equivalence, p.113.

(vi) Conway skein triple, p.113.

(vii) Drinfeld-Turaev quantization, pp.133-134.

(viii) Fox n-coloring, p.162.

(ix) Homotopy polynomial, p.194.

(x) Jaeger Composition Product, p.217.

(xi) Jones-Conway polynomial, pp.219-221.

(xii) Jones unknotting conjecture, pp.221-222.

(xiii) Kauffman bracket polynomial, pp.226-227.

(xiv) Listing polynomials, pp.240-241.

(xv) Markov’s braid theorem, p.251.

(xvi) Milnor’s unknotting conjecture, p.261.

(xvii) Montesinos-Nakanishi conjecture, pp.264-265.

(xviii) Positive link, p.308.

(xix) Reidemeister Theorem, pp.327-328.

(xx) Rotor, pp.337-338.

(xxi) Skein Module, pp.368-369.

14. Polynomial time complexity algorithm for computing coefficients of the Jones-Conway (Homflypt) and Kauffman polynomials of links, Abstracts AMS, 23(1), 2002, p.147.

15. Presentations od Skein Algebras, Abstracts AMS, 23(2), 2002.

16. Branched covers of tangles in three-balls (with M.Ishiwata and A.Yasuhara), in Japanese, Proceedings of the conference dedicated to S.Suzuki and T.Kobayashi on their 60th birthday, Tokyo, 2002, 157-164.

17. Symmetry of links and classification of lens spaces (with A.Yasuhara), in Japanese, Proceedings of the conference dedicated to S.Suzuki and T.Kobayashi on their 60th birthday, Tokyo, 2002, 165-169,

18. Burnside group of a link as an obstructions to the Montesinos-Nakanishi 3-move conjecture (with M. D¸abkowski), Abstracts AMS, 23(2), June 2002.

19. Rational moves on links measured by Burnside type groups (with M. D¸abkowski), Abstracts AMS, 23(2), June 2002.

20. Burnside obstruction to the Montesinos-Nakanishi 3-move conjecture. Proceedingas of the conference “Topology in Matsue” (June 24-28, 2002).

21. 4-moves and 4th Burnside group of links: Nakanishi and Kawauchi conjectures (with M. Dabkowski), Abstracts AMS, 23(4), 2002.

22. Number theoretical criterion for invariance of Fox p-colorings under n-rotation. Abstracts AMS, 24(1), 2003.

23. Variety of groups of knots (with M. D¸abkowski), Abstracts AMS, 24(2), 2003.

24. Derived group of a link group: three applications (with M. D¸abkowski), Abstracts AMS, 24(2), 2003.

25. Khovanov homology of links in I-bundles over surfaces (with M.M.Asaeda and A.S.Sikora), Report No. 46/2003, Mathematisches Forschungsinstitut Oberwolfach, p. 4.

26. Rotation and signature invariants (with M. D¸abkowski, M. Ishiwata and A,Yasuhara),

e- abstract (July 2004): http://www.math.kobe-u.ac.jp/HOME/nakanisi/KOOKseminarINT/ishiwata

27. Khovanov graph homology as a Hochschild homology of graphs, Abstracts of AMS, 26(4), 2005

28. Confluence of Khovanov homology and Hochschild homology, Abstracts of AMS, 27(1), p.157, 2006.

29. 5-move equivalence for links up to 9-crossings (with M.Ishiwata andM.K.Dabkowski), Extended abstract/slides Osaka, November 2005:

http://pal.las.osaka-sandai.ac.jp/ math/TopComp2005/TC2005programE.html http://pal.las.osakasandai.ac.jp/ math/TopComp2005/Slides/ishiwata.pdf

Selected Invited Talks

1. Topology Seminar, Gdansk University, Poland, December 18, 2009; Homologie quandli: graf obliczen i operacje homologiczne

2. Colloquium, Gdansk University, Poland, December 17, 2009; (Invited) Quandle- historyczne wprowadzenie i teoria ich homologii.

3. Knots in Washington XXIX, 30 years of Quandles, 10 years of Khovanov homology, December 5, 2009; The second quandle homology of Takasaki keis (quandles).

4. Colloquium, U.S. Naval Academy Annapolis, November 18, 2009; Homology of quandles: a toy or a powerful machinery?

5. Algebra and Topology Conference at University of Louisiana at Lafayette, November 1, 2009 (Plenary talk); Skein modules of 3-manifolds: from first homology to Khovanov homology.

6. AMS Special Session on Invariants of Knots and Links at the AMS meeting, Florida Atlantic University, Boca Raton, FL (2009 Fall Southeastern Meeting) October 30 – November 1, 2009; (Invited) Homology of Takasaki quandles.

7. Colloquium at University of Texas at Dallas; October 23, 2009; Classical roots and modern fruits of Knot Theory: from Gordian knot to Khovanov homology.

8. International Centre for Theoretical Physics, Trieste, Italy: Plenary talk at the Conference on Knot Theory and its Applications to Physics and Biology; (May 27, 2009)

Skein module motivation for Gram determinants of curves on surfaces.

9. International Centre for Theoretical Physics, Trieste, Italy: Series of 3 lectures at Advanced School and Conference on Knot Theory and its Applications

to Physics and Biology: Fox coloring, Burnside groups, skein modules and Khovanov categorification of skein modules; I (May 11, 2009); Fox coloring, Burnside groups, skein modules and Khovanov categorification of skein modules; II (May 12, 2009); Fox coloring, Burnside groups, skein modules and Khovanov categorification of skein modules; III (May 13, 2009);

10. Topology seminar, University of Virginia, April, 30, 2009; Algebra Situs: panorama of skein modules.

11. Lecture at Polish Professors Club, March 6, 2009, Kensington, MD; Klasyczne ´zr´od la teorii w¸ez l´ow (in Polish; Classical roots of Knot Theory)

12. Knots in Washington XXVIII, February 27 – March 1, 2009; Domination of knots and the Jones polynomial.

13. AMS Special Session on Categorification and Link Homology at the AMS 2009 National Meeting, Washington D.C., January 5-8, 2009; Gram determinants of planar states and Lagrangian tangles.

14. The Workshop ”The Mathematics of Knots: Theory and Application” Heidelberg, Germany, December 15-19, 2008; Plenary talk Skein module motivation for Gram determinants of planar curves

15. The International Conference ”Geometry and Topology in Low Dimensions”, CIRM in Luminy, France, November 17 -21, 2008, Gram determinants of planar curves: Skein Module motivation

16. Colloquium, Howard University, November 7, 2008; Gram determinants of planar curves: topological motivation

17. Topology seminar, Louisiana University, Lafayette, October 2008; Gram determinants in Knot Theory: skein module motivation

18. Topology seminar, Technical University in Athens, Greece, June 20, 2008 An introduction to Khovanov homology via Kauffman bracket polynomial of knots.

19. Conference on Algebraic and Geometric Topology June 09-13, 2008, Gdansk, Poland, Solution to Rodica Simion question on the Gram determinant of the type B Temperley-Lieb

algebra.

20. Topology Seminar, Bard College, NY, April 28, 2008 Quandles in Knot Theory; how to approach Nakanishi 4-move conjecture.

21. AMS Special Session on Knot and 3-Manifold Invariants at the 2008 Spring Southeastern Meeting Baton Rouge, LA, March 28-30; The Gram determinant of the type B Temperley-Lieb algebra and the determinant of the matrix of chromatic joins

22. Knots in Washington XXV; Dedicated to Herbert Seifert on his 100 birthday, December 7-9, 2007; Torsion in H^{2,v(G)−2}_{A2}(G) and its applications to Khovanov homology of adequate diagrams.

23. Knotting Mathematics and Art: Conference in Low Dimensional Topology and Mathematical Art Nov. 1-4, 2007, at University of South Florida, Tampa, FL, History of knot theory: art and science.

24. AMS Special Session on Topics in Mathematical Physics at the AMS meeting, Albuquerque, NM, October 13-14, 2007; Hochschild homology of Frobenius algebras via link diagrams; Khovanov homology

25. AMS Special Session on Invariants of links and 3-manifolds at the AMS/PTM International Meeting, July 31 - August 3, 2007, Warsaw, Poland; Hochschild homology of Frobenius algebras via link diagrams

26. Nagoya (NIT) topology seminar, June 30, 2007, Introduction to Khovanov homology via Hochschild homology and Taits graphs of links

27. Waseda University seminar, Tokyo, Japan, June 15, 2007; Introduction to Hochschild and Khovanov homologies

28. Seminar, International Centre for Theoretical Physics, Trieste, Italy, May 15, 2007; Definition of Khovanov homology from Kauffman bracket

29. Seminar, International Centre for Theoretical Physics, Trieste, Italy, May 9, 2007; Introduction to Khovanov homology of knots via Hochschild homology of algebras

30. BIRS workshop ”The many strands of the braid groups”, Banff, Canada, April 22 – 27, 2007; 2-braid intersection of Hochschild and Khovanov homologies

31. Knots in Washington XXIV; Dedicated to the memory of Xiao-Song Lin, April 13-15, 2007; Burnside groups of knots, tangle moves and their skein module deformations

32. AMS Special Session at Oxford, OH, March 15-18, 2007; Homology of dihedral quandles

33. Algebraic topology seminar, Warsaw, Poland, February 27, 2007, Jak zbudowac homologie grafow bazujace na nieprzemiennych algebrach (How to build homology of graphs with underlying noncommutative algebras)

34. Polish Mathematical Society seminar, Gdansk, Poland, February 23, 2007, Introduction to Khovanov homology (in Polish)

35. Algebraic topology seminar, Warsaw, Poland, February 20, 2007, Od homologii Hochschilda algebr do homologii Khovanova splotow (From Hochschild homology

of algebras to Khovanov homology of links)

36. AMS Special Session on Knots, 3-manifolds, and Their Invariants at the National AMS Meeting in New Orleans, January 5-8, 2007, Hochschild homology, cones, and combinatorial patterns in Khovanov type graph homology

37. Workshop: Knots and Braids, Banach Center, Warsaw, Poland Dec. 11-17, 2006; From Reidemeister moves to Quandle homology

38. Topology student seminar, Gda´nsk University, December 8, 2006; Od 3-kolorowania Foxa do Quandli II (From Fox 3-coloring to Quandles II).

39. Colloquium, Gda´nsk University, December 7, 2006; Dwie drogi do homologii Khovanova: przez wielomian Jonesa i przez homologie Hochschilda

(Two paths to Khovanov homology: through Jones polynomial and through Hochschild homology).

40. Geometry and Topology seminar, Gda´nsk University, December 6, 2006; Homologie Dihedralnych Quandli (Homology of Dihedral Quandles)

41. Topology student seminar, Gda´nsk University, December 1, 2006; Od 3-kolorowania Foxa do Quandli: I (from Fox 3-coloring to Quandles: I).

42. Knots in Washington XXIII; Quandles, their homology and ramifications, November, 2007 Homology of dihedral quandles II

43. Conference on Categorification in Algebra and Topology, September 7-10, 2006, Uppsala, Sweden; Hochschild homology as Khovanov homology of torus links

44. Geometry and Topology of Low Dimensional Manifolds, A conference in honour of Prof. Mara Teresa Lozano, Prof. Jos Mara Montesinos, Prof. David Singerman, 31 August – 2 September 2006, El Burgo de Osma, Spain, Plenary talk, Khovanov homology of links and Hochschild homology of algebras

http://www.mai.liu.se/LowDim/abstract.html#Przytycki

45. Knots in Washington XXII, May 5-7, 2006, Combinatorial patterns in Khovanov type graph homology motivated by Hochschild homology

46. AMS Special Session on Quantum invariants of knots and 3-manifolds, Durham, NH, April 22-23, 2006, Combinatorial patterns in Khovanov type graph homology

47. Geometric Topology seminar, Columbia University, March 24, 2006, Hochschild homology and combinatorial patterns in Khovanov type graph homology.

48. AMS Special Session on Quantum Invariants of knots and 3-manifolds, San Antonio, TX, January 12-15, 2006. Confluence of Khovanov homology and Hochschild homology.

49. Knots in Washington XXI: Skein modules, Khovanov homology and Hochschild homology, GWU, December 9-11, 2005. Confluence of Khovanov homology and Hochschild homology: Application to truncated polynomial algebra.

50. Colloquium, Boise State University; November 4, 2005, From Khovanov homology to Hochschild homology and back in 50 minutes.

51. AMS Special Session on Invariants of Graphs and Matroids, October 8-9, 2005, Bard College, Annandale-on-Hudson; Khovanov graph homology as a Hochschild homology of graphs.

52. AMS Special Session on Invariants of Graphs and Matroids, October 8-9, 2005, Bard College, Annandale-on-Hudson; Introduction to Khovanov homology and graph homology (with M. Pabiniak and R. Sazdanovic).

53. Colloquium, George Mason University, September 30, 2005, Open problems in Knot Theory which everyone can try to solve,

54. Workshop on Khovanov Homology and Hochschild homology, Univ. Iowa, September 15-21, 2005, Khovanov Homology and Hochschild homology (plenary talk)

55. Topology seminar, U. Iowa, Sept. 20, 2005, Introduction to Khovanov homology and Hochschild homology,

56. MANIFOLDS and their MAPPINGS - 5th International Siegen Topology Symposium Monday, July 25, - Saturday, July 30, 2005; Relation between Khovanov homology and cyclic homology of Connes,

57. AMS-IMS-SIAM Summer Research Conferences in the Mathematical Sciences, “Quantum topology — contemporary issues and perspectives”, the Snowbird Resort, Snowbird, Utah, June 4 - June 10, 2005, Two talks:

(i) Panorama of skein modules,

(ii) From Kauffman bracket to Khovanov homology and Connes cyclic homology

58. Colloquium, University of South Florida, April 1, 2005 Old problems – new solutions in Knot Theory.

59. Georgetown colloquium, Monday, March 21, 2005; Open problems in Knot Theory which everyone can try to solve.

60. Conference on Braids, Links, and Mapping Class Groups (Joan Birman’s retirement conference); March 17-20, 2005; Plenary talk (Invited)

Skein module deformation of rational moves: Invariants motivated by a braid group action on Takasaki’s Kei.

61. Colloquium, Dartmouth College, March 3, 2005, Open problems in Knot Theory which everyone can try to solve.

62. Geometry seminar, Dartmouth College, March 3, 2005, Khovanov type homology for twisted I-bundles over surfaces

63. Port City Topology Conference, Mobile, Alabama, February 26-27, 2005; Kei, Burnside groups and skein module deformation of rational moves

64. Knots in Washington XX: 60th birthday of Louis H. Kauffman, GWU, February 11-13, 2005. Survey on the Kauffman bracket skein modules of 3-manifolds

65. Topology seminar, Waseda University, Tokyo, January 27, 2005; Kei, Burnside groups, Fox colorings and tangle moves.

66. Topology Seminar, RIMS, Kyoto University, January 24, 2005; Fox colorings, Burnside groups and Kei as obstructions to rational moves.

67. Tsuda College, Tokyo, January 20, 2005; Rational moves: seven elementary open problems.

68. Tokyo Institute of Technology, January 19, 2004, Categorification of Kauffman skein relation: Khovanov homology and skein modules.

69. Workshop “Topology of Knots VII”, TWCU, Japan, Dec. 23, 2004. Obstructions to tangle embeddings modulo rational moves

70. Topology seminar, University of Tokyo, Dec. 21, 2004 Khovanov Homology: categorification of the Kauffman bracket relation

71. Topology seminar, Nippon University, Dec. 18, 2004, Constructing fundamental groups of branched coverings – detecting non-orderability.

72. Williams College, Nov 19, 2004, Seven elementary open problems in Knot Theory.

73. Knots inWashington XIX: Topology in Biology 2, Georgetown University and GWU, November 12-14, 2004, An introduction to Khovanov homology categorification of skein modules.

74. AMS Special Session on Braids and Knots, October 16-17, 2004, Albuquerque, New Mexico, Kauffman-Harary Conjecture for Montesinos links and closed 3-braids

75. AMS Special Session Categories and Operads in Topology, Geometry, Physics and Other Applications, October 16-17, 2004, Albuquerque, New Mexico, Categorification of the Kauffman bracket skein module of F × I

76. Topology Seminar, University of Uppsala, Sweden, September 28, 2004; Survey of skein modules of 3-manifols.

77. Knots in Vancouver July 18-23, 2004, Khovanov Categorification of the Kauffman bracket skein module.

78. MSRI-PIMS Summer Graduate Programme: Knots and 3-manifolds. Series of 3 talks (Vancouver July 2004).

1. (July 15) Skein modules and Khovanov Homology 1: Rational moves and Burnside groups and skein module deformations.

2. (July 16) Skein modules and Khovanov Homology 2: Survey of skein modules. 3. (July 17) Skein modules and Khovanov Homology 3: Khovanov homology as a categorification of the Kauffman bracket.

79. Knots in Washington XVIII, GWU, May 28-30, 2004, Thickness of Khovanov homology of k-almost alternating links.

80. Mathematical circles, Mobile Alabama, March 29, 2004; Why knot?

81. Columbian Fellow lecture, March 24, 2004; Classical roots of Knot Theory

82. Colloquium, University of Texas at Dallas, March 5, 2004; How Burnside groups have found their place in Knot Theory

83. The third International Workshop: Graphs – Operads – Logic, Oaxtepec, Cuautitlan, Mexico, February 4-13, 2004 (three plenary talks);

1. 10 elementary knotted problems.

2. Fox colorings and their noncommutative generalizations.

3. Lagrangian tangles and imprisoned colors.

84. AMS Special Session on Low-Dimensional Topology, Phoenix, AZ, January 7-10, 2004; #993, Khovanov homology of links in I-bundles over surfaces

85. Knots in Washington XVII, GWU, December 19-21, 2003; My first and hundredth papers: surfaces and periodicity.

86. Borders in 3-Dim Topology, December 5–7, 2003 The Ohio State University, Columbus, OH Skein modules and stratified Khovanov homology.

87. Workshop on the interaction of finite type and Gromov-Witten invariants Dates: Nov 15-20, 2003, Banff International Research Station). Khovanov homology of tangles and I-bundles over surfaces.

88. Mini-Workshop at Oberwolfach – Quantum Topology in Dimension Three, Germany, October 19-25, 2003, Khovanov homology of links in I-bundles over surfaces.

89. Colloquium, University of Iowa, October 2, 2003, Old problems – new solutions in the Knot Theory 90. Topology seminar, University of Iowa, September 30, 2003,

Skein module motivation for Khovanov homology

91. Knots in Poland, July 2003, Banach Center (Warsaw and Bedlewo).

1. 3-moves, 4-moves and rational moves on links, obstructions and conjectures.

2. Introduction to Skein Modules.

92. Conference–workshop June 2-6, 2003, at SUNY Potsdam).

Talk 1: Unexpected connections between Burnside groups and Knot Theory.

Talk 2: Skein module deformations of rational moves: landscape of skein modules.

93. Knots in Washington XVI; May 5-7, 2003, University of Maryland, College Park, Kauffman-Harary Conjecture holds for Montesinos knots.

94. AMS Special Session in Low dimensional topology at the Courant Institute, NY April 12-13, 2003 Derived group of a link group: three applications.

95. The geometric topology session of the 2003 Spring Topology and Dynamical Systems Conference. March 20- 22 at Texas Tech University in Lubbock, Texas.

Unexpected connection between Burnside groups and Knot Theory.

96. AMS Special Session on Low Dimensional Topology, Baton Rouge, Louisiana, March 14-16, 2003 Variety of groups of knots.

97. The JAMI (Japan-U.S. Mathematics Institute) Spring Conference, JHU, Baltimore, 6 - 16 March 2003, Ideal obstructions to embedding tangles into links.

98. Colloquium, University of Virginia, February 13, 2003

Unexpected connections between Burnside groups and Knot Theory.

99. Topology seminar, University of Virginia, February 13, 2003 Rotors in Graph Theory and Knot Theory.

100. Topology seminar, JHU, February 10, 2003, Unexpected connections between Burnside groups and Knot Theory: solution to Nakanishi conjectures.

101. AMS special session on Primes and Knots (#983) Baltimore, January 15-18, 2003. Number theoretical criterion for invariance of Fox p-colorings under n-rotation.

102. Knots in Washington XV, Japan - USA workshop in Knot Theory II, January 10-15, 2003, Action of braid groups related to double branched covers.

103. Conference in Low Dimensional Topology to celebrate the sixtieth birthday of Francisco Javier ”Fico” Gonzalez Acuna December 9-13, 2002, Universidad Autonoma de Yucatan, Merida, Mexico. How Burnside groups have found their place in Knot Theory. Invited plenary talk.

104. Topology seminar, SUNY at Buffalo, November 15, 2002, Burnside obstructions to Rational moves on links.

105. Colloquium, SUNY at Buffalo, November 14, 2002, Unexpected connections between Burnside groups and Knot Theory.

106. AMS Special Session on Invariants of Knots and Low-Dimensional Manifolds, Orlando, FL, November 9-10, 2002, Meeting #982

4-moves and 4th Burnside group of links: Nakanishi and Kawauchi conjectures.

107. Conference/workshop July 8-12, 2002, at SUNY Potsdam. Georgia Benkart, Louis Kauffman, and Kazem Mahdavi (organizers). Plenary speaker.Solution to the Montesinos-Nakanishi 3-move conjecture.

108. Topology Seminar, TWCU, Tokyo, Japan, July 1, 2002; 3-moves, Burnside groups and cubic skein modules.

109. Topology Seminar, Waseda University, Tokyo, Japan; July 5 (Friday) 2002. Fox 3-colorings and Burnside groups in Knot Theory.

110. Invited plenary speaker, Topology in Matsue (June 24-28, 2002) International Conference on Topology and its Applications Joined with Second Japan-Mexico Topology Symposium (Shimane University and the Mathematical Society of Japan); Burnside obstruction to the Montesinos-Nakanishi 3-move conjecture.

111. AMS Special Session on Quantum Topology, Portland, Oregon, June 20-22, 2002. Rational moves on links measured by Burnside type groups.

112. Pozna`n University topology seminar, June 4, 2002. Lagranzanowskie suply i przeszkody Burnside w teorii wezl´ow.

113. Gda´nsk topology seminars May 27-28, 2002 (2 invited talks):

1. W Poszukiwaniu nietrywialnego w¸ez la z trywialnym wielomianem Jonesa.

2. Czy ten supe l jest cz¸e´sci¸a Twojego splotu?

114. Gdansk topology conference (Jankowski memorial) May 24-25, 2002; Solution to the Montesinos-Nakanishi 3-move conjecture.

115. Knots in Washington, XIV, Conference on Knot Theory and its Ramifications, May 17, 2002, at the George Washington University;

116. II Workshop ‘GRAPHS-OPERADS-LOGICS’, Cuautitl´an, M´exico, May 5-12, 2002 (Invited for series of four talks).

1. How much of the coloring can be caged in a tangle?

2. Skein algebra of a product of a surface and the interval

3. Knotting of ideas from algebra geometry and topology

4. From combinatorics of knot diagrams to the algebraic topology based on knots

117. Colloquium, Ohio State University, Columbus Ohio, May 2, 2002, Old conjecture – new solutions in the Knot Theory

118. Knots in Montreal – hyperbolic volume conjecture (conference) April 19-21, 2002, UQAM, Montreal, Canada. The Montesinos-Nakanishi 3-move conjecture is solved.

119. Topology seminars, April 1, 8, University of Maryland.

1. Burnside obstructions to the Montesinos-Nakanishi 3-move conjecture.

2. Lagrangians of tangles and rotors of links.

120. Workshop on Quantum Topology, March 18-22, 2002 in Warwick, Quantum obstructions to tangle embeddings.

121. AMS Special Session on Quantum Topology in Dimension Three; Ann Arbor, Michigan, March 1-3, 2002

Presentations of Skein Algebras.

122. AMS special session on Computational Topology San Diego, California, January 8, 2002; Polynomial time complexity algorithm for computing coefficients of the Jones-Conway (Homflypt) and Kauffman polynomials of links.

123. Knots in Washington, XIII, Conference on Knot Theory and its Ramifications, Dec. 16, 2001, at the George Washington University; Rotors and the homology of branched double covers of links and tangles.

124. AMS Special Session on Quantum Topology, Columbus at OSU; September 21-23, 2001; Lagrangian approximation of Fox p-colorings of tangles; Fox approximation of rational pq -moves.

125. Research Institute for Mathematical Sciences (RIMS), Kyoto University; workshop on invariants of knots and 3-manifolds

1. Seminar talk; RIMS, September 11, 2001; Skein modules with a cubic skein relation: properties and speculations.

2. Workshop talk, RIMS, September 18, 2001; Symplectic structure on colorings, Lagrangian tangles and its applications.

126. ”New Techniques in Topological Quantum Field Theory” Workshop; Calgary, Canada, August 2001; Symplectic structure on colorings of tangles

127. Knots in Washington, XII, Conference on Knot Theory and its Ramifications, May 10-12, 2001, at the George Washington University; Lagrangian approximation of local moves on links.

128. AMS Special Session on Topology of links at the AMS meeting at UNLV, Las Vegas, April 21-22, 2001, Symplectic form on t-colorings of tangles.

129. Knots in Montreal (conference) April 7-8, 2001, UQAM, Montreal, Canada. Lagrangian tangles in Fox coloring spaces and their t-deformations.

130. The First InternationalWorkshop on Graphs – Operads – Logic, Cuautitl´an, M´exico, March 12-16, 2001. Three talks under the general title Algebraic Topology Based on Knots.

(1) Open problems in knot theory that everyone can try to solve.

(2) Lagrangian approximation of Fox p-colorings of tangles.

(3) Historical Introduction to Skein Modules.

131. KNOTS, LINKS and MANIFOLDS - 4th International Siegen Topology Symposium - January 4–8, 2001, Siegen Germany Symplectic form on colorings of tangles: the structure theorem and applications.

132. Warsaw University Topology seminar; December 12, 2000, Przestrze´n symplektyczna kolorowa´n n-sup la.

133. AMS Special Session on The topology of 3-manifolds Columbia University, NY, November 2000, Symplectic structure on colorings of tangles

134. AMS Special Session on Diagrammatic Morphisms in Algebra, Category Theory, and Topology, San Francisco State University on October 21-22, 2000 Symplectic structure on Colorings and Lagrangian tangles.

135. Topology seminar(s), Gdansk University, Poland, May 12-13, 2000, Two (not so easy) talks on Algebra Situs.

136. Colloquium, Polish Mathematical Society and Banach Center, Warsaw, Poland; May 11, 2000 Skein modules of 3-manifolds: from quantized homology to the Kontsevich Theorem on Vassiliev invariants.

137. Colloquium, Lviv University, Ukraine, May 7, 2000;Algebraichna topologia shcho bazuetsa na vuzlach (Algebraic topology based on knots).

138. AMS Special Session on Quantum Topology April 14-16 2000; Lafayette, Louisiana. Are the Reshetikhin-Turaev-Witten invariants determining the volume of a hyperbolic 3-manifold?

139. 5. Topology seminar(s), Gdansk University, Poland, March 31 - April 1, 2000 ˙Three easy talks on knot theory and skein modules.

140. 6. Knot Theory Seminar, Banach Center, Warsaw, Poland; March, 22, 2000; Hopf algebra structure of Vassiliev-Gusarov skein modules of Knots and Links.

141. Colloquium, Gdansk University, Poland, March 6, 2000 Skein modu ly: Od 3-kolorowania do Twierdzenia Koncewicza o niezmiennikach Wasiliewa, in Polish (Skein modules: from the 3-coloring to the Kontsevich Theorem on Vassiliev invariants)

142. Colloquium, Case Western Reserve University, February 25, 2000; Algebra Situs – how to build an algebraic topology from knots.

143. Students’ Seminar, Case Western Reserve University, February 24, 2000; Elementary invariants of knots: from Gauss and Listing to Fox and Jones.

144. Knots in Washington, X, Japan - USA ; workshop in Knot Theory, January 23-30, 2000; Symplectic and unitary quotients of Burau representation, and 3-move and t3, ¯t4-move conjectures.

145. Scottish Topology Seminar, December 3, 1999, Edinburgh, Scotland, UK, Algebra situs: an example from knot theory.

146. Geometry-Topology Seminar, University of Warwick, England, November 18, 1999, Skein modules and geometry of 3-manifolds.

147. Cambridge Topology Seminar, November 15, 1999, University of Cambridge, Skein modules of 3-manifolds with cubic relations.

148. Geometry-Topology Seminar, University of Maryland (College Park), October 25, 1999 An overview of skein modules.

149. Topology Seminar (GWU), October 21, 1999. The first coefficient of Homflypt and Kauffman polynomials: Vertigan proof of polynomial complexity using dynamic programming.

150. Knots in Washington, IX, Conference on Knot Theory and its Ramifications, September 24-25, 1999, at the George Washington University Positive knots and their properties.

151. AMS Special Session on The Development of Topology in the Americas, Austin, Texas, October 8-10, 1999. Little and Haseman – early American tabulators of knots

152. Topology Seminar, Kyoto Sangyo University; August 4, 1999 Skein modules of 3-manifolds: torsion reflection of incompressible surfaces

153. The 46th Japan Topology Symposium at Hokkaido University; “One hour invited talk” July 26–29, 1999; Sapporo (Hokkaido University). The Kauffman bracket skein algebra of a surface times the interval has no zero divisors

154. Topology Seminar, Waseda University, Tokyo, July 22, 1999. The Kauffman bracket skein module.

155. Topology Seminar, Chuo University, Tokyo, July 7, 1999. Algebraic topology based on knots.

156. Topology Seminar, Hiroshima University, July 6, 1999. Torsion in skein modules.

157. Topology Seminar, Tokyo Woman’s Christian University, June 26, 1999; Kauffman bracket skein module of a connected sum of 3-manifolds.

158. Topology Seminar, Osaka University, June 21-22, 1999. Algebraic topology based on knots, I and II.

159. AMS Special Session on Noncommutative Geometry, Quantum Groups, and Applications, Denton, Texas, May 19-22, 1999, Homotopy quantization of skein modules.

160. Knots in Washington, VIII, conference on knot theory and its ramifications, April 30, May 1 1999, Homotopy skein modules of 3-manifolds: an example in Algebra Situs.

161. AMS Special Session on Knot and 3-Manifolds, Buffalo, New York, April 24-25, 1999, q-homotopy skein module of 3-manifolds; properties and applications.

162. AMS Special Session on symmetries of Knots and Three-manifolds, Las Vegas, Nevada, April 10-11, 1999. Homotopy skein module, dichromatic polynomial and symmetry.

163. International Conference on Geometry and Topology, 5-12 January, 1999, Technion, Haifa, Israel. Torsion in the Kauffman bracket skein module of 3-manifolds and use of incompressible surfaces and hyperbolic structure in torsion detection.

164. Topology seminar, Boise State University, December 15, 1998.

165. Fall 1998 Louisiana Topology Conference (plenary speaker), Nov. 14-15, 1998. Algebra Situs

166. Knots in Washington, VII ”Topology in Biology”, October 23-24, 1998, at Georgetown University. Torsion in skein modules.

167. Knots in Hellas – International Conference on Knot Theory and its ramifications, Delphi (Greece) August 7-15, 1998; Algebra Situs - algebraic topology based on knots

168. Topology seminar, University of Frankfurt, July, 1998.

169. AMS Special Session on Quantum Topology during the Central Section Meeting, Kansas State University, March 27-8, 1998; S2,1(Hn#Hm;Z[A±1],A)

170. AMS Special Session on Low-dimensional topology at the Spring meeting of the American Mathematical Society, March 20-21 1998, in Louisville, KY;

Torsion in the Kauffman bracket skein module of a 3-manifold and use of a homology group and hyperbolic structure in torsion detection.

171. Knots, Braids, and Mapping Class Groups: A Conference in Low-Dimensional Topology in Honor of Joan Birman’s 70th Birthday, Columbia University/Barnard College, New York, March 14–15, 1998.

Algebraic topology based on knots: a case study in the history of ideas.

172. Knot Theory Days (Knots in Washington); Sixth conference on knot theory and its ramifications, Feb. 7-9, 1998, U.S. Naval Academy Annapolis; On the Jones polynomial of a torus link in a solid torus.

173. International Low Dimensional Topology Conference, Universidade Da Madeira, Portugal, January 11-17, 1998; Panorama of skein modules.

174. Colloquium, Boise State University, December 1997; Symmetric knots.

175. Knots in Washington; Fifth conference on knot theory and its ramifications, November 22, 1997, University of Maryland at College Park; Torsion in skein modules: Theorems, Conjectures and Speculations.

176. First Graduate Fair Talk, Bowie State University, October 30, 1997. Elementary invariants of knots: from Gauss and Listing to Fox and Jones.

177. Knots in Washington; Fourth mini-conference on knot theory and its ramifications, April 5, 1997, University of Virginia; Listing’s polynomial of graphs and link diagrams.

178. AMS Special Session on Invariants of 3-manifolds, Memphis, Tennessee, March 21-22, 1997; The Kauffman bracket skein algebra of links and arcs.

179. Knots in Washington: Third conference on knot theory and its ramifications, October 19, 1996;

Kauffman bracket skein algebra of a product of a surface and interval is an integral domain.

180. Colloquium, University of Maryland at College Park, Sept. 20, 1996; Introduction to Algebraic Topology Based on Knots.

181. Knots 96, Tokyo, Japan, July 1996; Algebraic topology based on knots.

182. AMS-IMS-SIAM Joint Summer Research Conference: Quantization, Mount Holyoke College, July 8, 1996; Skein algebras of 3-dimensional manifolds.

183. AMS Special Session on Low-dimensional topology, Baton Rouge (LSU), April 19-21, 1996; Lissajous knots, billiard knots and their symmetry.

184. Colloquium, University of South Alabama, April 18 1996; Elementary invariants of knots: from Gauss to Jones.

185. Knots in Washington; Second mini-conference on knot theory and its ramifications, March 30, 1996; What is new in skein modules?

186. AMS Special Session on Topology of 3-manifolds, Iowa City, March 22-23, 1996; The Kauffman bracket skein algebra of links: examples and speculations.

187. Colloquium, American University, March 1996; 3-colorings and other elementary invariants of knots.

188. Topology Seminar, Columbia University, November 10, 1995; Kauffman bracket skein algebra of a torus cross interval.

189. Knots in Washington; mini-conference on knot theory and its ramifications, October 1995;

(i) Knots and Braids in Gauss’ notebooks,

(ii) Search for different links with the same Jones’ type polynomials.

190. Colloquium, GWU, October 1995. Lissajous knots, billiard knots and their symmetry.

191. Mini-conference on knots and braids, G¨ottingen (Germany), July 1995. Skein algebra of a surface cross interval is a q-deformation of the symmetric homology.

192. Colloquium, Copenhagen University, June 1995. 3-colorings and other elementary invariants of knots.

193. University of California at Davis, Topology seminar, May 1995 Algebraic topology based on knots.

194. Plenary Talk, Cascade Mountains Topology Conference, May 1995 Boise State University; Algebraic topology based on knots

195. U.C.Berkeley (Subfactor Seminar), May 5, 1995. Symmetry of knots: Lissajous and billiard knots;

196. MSRI (Berkeley), April 1995 Algebraic topology based on knots.

197. Topology Seminar, Warwick University, December 1994. 3-colorings and other elementary invariants of knots.

198. Fluid Mechanics Seminar, University College London, December 1994; 3-colorings and other elementary invariants of knots.

199. Colloquium, Boise State University, November 1994; 3-colorings and other elementary knot invariants

200. International Conference in Low Dimensional Topology: knots, 3-manifolds and application, Marseille-Luminy, July 20, 1994; Algebraic topology based on knots.

201. Topology seminar, Toulouse (France), July 13, 1994; Different links with the same Jones type polynomials.

202. Topology seminar, Strasbourg (France), May 1994; Algebraic topology based on knots.

203. Colloquium, Nantes (France), May 1994; Algebraic topology based on knots.

204. Grenoble: e.g. Fourier Institute seminar. April-May 1994;

1. Algebraic topology based on knots,

2. 3-coloring and other elementary invariants of knots

205. The first Pulikowski’s Lecture, 200 lat teorii w¸ez l´ow, (Two hundred years of knot theory. (Polish) ), Pozna´n, March 1994.

206. Topology seminar, G¨ottingen (Germany), February 1994.

207. Odense University (Denmark), Colloquium, December 1993; Algebraic topology based on knots.

208. Universite Paris VII, Topology seminar, September 1993.

209. Workshop on Conformal Field Theory, Operator Algebras and Low-Dimensional Topology, Warwick, August 1993,

210. International Meeting on Knots and Links, Siegen, Germany, July 1993,

211. University of California at Riverside, Topology seminar, April 1993,

212. AMS special session on Low Dimensional Topology, Washington, April 1993,

213. Columbia University, New York, Topology seminar, April 2, 1993,

214. IUPUI-Indianapolis, Colloquium, March 29, 1993,

215. Conference on Quantum Topology, Kansas State University, March 1993,

216. Aarhus University, Denmark, Topology/Geometry Seminar, March 16, 1993,

217. Isaac Newton Institute for Mathematical Sciences, Program on Low Dimensional Topology and Quantum Field Theory, (Cambridge, November 1992).

218. University of Iowa, Colloquium (November 1992).

219. AMS special session on Knots and Topological Quantum Field Theory, (Dayton, October- November 1992) Nov 1, 1992.

220. Colloquium, Odense University (Denmark), 22 October 1992.

221. Georgia Topological Conference, Athens, August 1992.

222. Low-Dimensional Topology Conference, UT Knoxville, May 1992.

223. AMS special session on New Invariants of Links and 3-manifolds, Bethlehem, April 1992.

224. Colloquium, Memphis State University, February 1992.

225. Workshop on Jones-Witten Invariants of 3-manifolds, Guanajuato, Mexico, December 1991.

226. Colloquium, Boise State University, November 1991.

227. XXIV Mexican National Congress of Math., November 1991.

228. AMS special session on Knotting Phenomena in Natural Sciences, Santa Barbara, November 1991.

229. UT Knoxville, Topology seminar, October 1991.

230. AMS-IMS-SIAM Joint Summer Research Conference on Graph Minors, Seattle, July 1991.

231. UC Riverside, Colloquium, April 1991.

232. University of Southern California, February 1991.

233. UBC, Vancouver, Special Topology Seminar, September 10, 1990. Skein modules of links in 3-manifolds.

234. Columbia University, Topology Seminar, May 1990. Skein module of links in F × I.

235. OSU (Columbus), April 9, 1990. Skein module of links in a handlebody.

236. Institute for Advanced Study, Members Seminar, February 26, 1990.

237. Michigan State University, October 1989.

238. University of Calgary, May 1989.

239. Columbia University, April 1989.

240. AMS special session on Knot Theory and Algebraic Geometry in the Large, Worcester M.A., April 1989.

241. University of Southern California, December 1988.

242. California Institute of Technology, December 1988.

243. Lehigh University Geometry and Topology Conference, May 1988. Skein modules of 3-manifolds.

244. Montreal (Univ. du Quebec), May 1988.

245. Montreal (Univ. du Quebec), January 1988.

246. Corvallis, Oregon, July 1987.

247. New York (Columbia Univ.-Courant Institute), April 1987.

248. Houston (Rice Univ.), April 1987.

249. Austin, Texas, April 1987.

250. Karcher Special Lecture, University of Oklahoma, Norman, Oklahoma, April 7, 1987; New invariants in Classical Knot Theory,

251. Karcher seminar, April 8, tk-moves on Links

252. Karcher seminar, New polynomial invariants and periodic links, April 10, 87.

253. AMS special session on Low Dimensional Topology (Honolulu, March 1987).

254. AMS special session on Geometric Topology (Logan, October 1986).

255. Colloquium, UBC, Vancouver, October 1986. New invariants in Classical Link Theory

256. AMS Conference on “Artin’s Braid Group” (Santa Cruz, July 1986). Conway formula for knot polynomials;

257. Ljubljana University (Slovenia), June 1986. 258. Zaragoza University, Spain, February 1986.

259. Ruhr-University (Bochum), September 1985.

260. Oberwolfach, September 13, 1985; Invariants of links of Conway type: algebras, polynomials, and signatures (joint work with P.Traczyk).

261. Topology seminar, November 9-10, 1984, Warsaw, Poland, Niezmienniki Jonesa (Invariants of Jones).

262. Warwick University, July 1984; n-relator manifolds with incompressible boundary

263. Durham (England), July 1984; Searching for a smallest volume hyperbolic manifold

264. Zaragoza University, Spain, May 29, 1984.

265. Oberwolfach, September 1983.

266. Plenary talk at the meeting of the Polish Mathematical Society after accepting the Kuratowski Prize, Warsaw August 1983,

267. Zaragoza University, Spain, October 1982.

268. AMS special session on Low Dimensional Topology (Pittsburgh PA, August 1981).

269. International conference on Geometric Toplogy, Aug 24 – Sept. 2, 1978.

Service

1. University Committee service:

(a) CSAS Committee on graduate studies, 2005-2006,

(b) Senate Research Committee, 2005 - 2006,

(c) Committee to select Columbian College fellow, 2003-2004

(d) The University Committee on Research (UCR), 2003-2006, (including UFF and Dilthey prizes)

(e) Advisory Council on Research; 2000–2003

(f) Research Committee of Faculty Senate 2000-2001

(g) Patent and Scholarly Works Panel (March, 2001)

(h) Member of the committee (CSAS) selecting the award winners for 1997-1998 Exemplary Paper Award

2. Department Committee service:

(a) The Undergraduate Program Committee (1995-96).

(b) Department of Mathematics Ad Hoc Committee for fundraising (1995-96).

It prepared the departmental response in connection with the 175th anniversary of the university fundraising campaign.

(c) Ad Hoc Scheduling Committee (1996).

(d) Department’s Committee for the proposed University’s Computational Sciences Program

(1996-1999).

(e) The Graduate Committee (1996-1998).

(i) Active participant in the recruitment of new graduate students.

(ii) Master and PhD Preliminary Written Examination coordinator. Grader of written examination in Topology (with Y.Rong); two examinations per year.

(f) Colloquia Chair (and member of Personnel Committee) 1998-99.

(g) The Graduate Committee (2000-2004).

(i) Recruting Com. (2000).

(h) Outside Chair search committee (2005-2006).

(i) Poster presentations

(u) Classical roots of Knot Theory, Scholars Showcase, GWU, March, 1998.

(uu) Algebra Situs, Scholars Showcase, GWU, January, 1999.

(uuu) Research Gallery of Inauguration Week’s Research Day (Wednesday, November 14th);

(t) Putnam training session. November 29, 2000.

3. Community Service

(a) Four lectures in mathematics for high school students in the Polish Saturday’s school (Washington); (Spring 1996).

(b) Six lectures in mathematics for high school students and three lectures for middle school students in the Polish Saturday’s school (Washington); (Spring 1997).

(c) Consultation. Polish edition of Scientific American (“W ´swiecie nauki”).

(d) Mentoring:

Doug Bullock (NSF postdoc, 1997-8),

Akira Yasuhara (Japanees Academy of Science postdoc, 1999-2001),

Makiko Ishiwata (visiting graduate student, from TWCU, Japan, 2001, and March/April 2002, visiting after PhD, September 2005),

Marta M. Asaeda (postdoc at UMCP, but practically she was my postdoc at GWU; 2001- 2003).

(e) NSF panels:

(i) NSF panel in Low Dimensional Tolopogy, February 15-17, 2007.

(ii) NSF Panel on NSF/CBMS Regional Research Conferences, June 8-9, 2007.

(f) Member of W.A.S. judging panel at the Paint Branch High School Science EXPO: Friday December 14th, 2007.

DESCRIPTION of RESEARCH INTERESTS

J´ozef H. Przytycki

Classical knot theory, topology of 3-manifolds, algebraic topology based on knots and related topics (e.g. graph theory, hyperbolic geometry, universal algebras, statistical mechanics, representations of Lie algebras and Hopf algebras, Hecke algebras, Khovanov homology, topological quantum field theory, character varieties, Hochschild homology, cyclic homology, history of topology). My goal is to build an algebraic topology based on knots; that is a consistent theory in which links play the role of cycles, skein modules the role of homology groups and link invariants the role of cohomology.

1. Generalizations of the Jones polynomial.

In 1984, I discovered (with P.Traczyk) a 2-variable generalization of the Jones polynomial (it was discovered independently by P.Freyd and D.Yetter, J.Hoste, R.Lickorish and K.Millett, and A.Ocneanu). Our main idea was to construct a universal algebra (which we called the Conway algebra) which utilize the skein relation observed by Conway and Jones. Any Conway algebra yields a link invariant, in particular we obtained the generalized Jones polynomial and a polynomial of infinitely many variables [14],[15]. I proved that the polynomial of infinite many variables can be used to obtain an invariant of link homotopy which sometimes works better than the generalized Jones polynomial [59]; it was conjectured before that such an invariant does not exist. We analyzed (with P.Traczyk) the properties of Conway algebras and their relations with the signature of links. We proved that the Tristram - Levine signature is, essentially, the skein invariant and we conjectured the existence of “the supersignature” which generalizes the Tristram - Levine signature and could be used to prove the Milnor’s unknotting conjecture (theorem) for positive braids [15].

2. Search for different links with the same Jones type polynomials: cabling, rotors, spectral parameter tangles.

I proved in 1986 that the (2, k) cables of knot mutants have the same skein (generalized Jones) polynomial. I showed also that knots K1#K2 and K1# − K2 cannot be distinguished by

considering skein or Kauffman polynomials of their satellites [23] (the above results were also discovered independently by R.Lickorish). These results can be used as a criterion to check

whether polynomial invariants obtained from representations of some “nonstandard” Lie algebras give genuinely new link invariants and whether Vassiliev-Gusarov invariants are genuinely

better than Jones type polynomials. Furthermore the above result can be used (as observed by J.Kania-Bartoszynska and R.Lickorish) to construct different 3-manifolds with the same

Witten and Reshetikhin-Turaev invariants. I worked with R.Anstee and D.Rolfsen on generalized mutation (“rotation”) of links and we proved several properties of rotants [20]. Recently I showed that rotors and examples obtained by Jones (different links with the same Jones type polynomials) using spectral parameter tangles have a common generalization [42,47]. The spectral parameter tangle corresponds to the spectral parameter in the Yang-Baxter equation. Further development of this concept is described in [7p].

3. Applications of Jones type polynomials: periodic links, Lissajou knots, billiard knots, braid index.I was working on periodic links and I found criteria for n-periodic links using the skein (Homflypt, generalized Jones) and Kauffman polynomials [22]. Recently I found a simple proof of

the powerful Traczyk-Yokota criteria of knot periodicity and a version of these criteria which uses the Kauffman polynomial [43]. I found also applications of Vassiliev knot invariants to study of knot’s periodicity [38].

I analyzed Lissajous (and billiard) knots and I found that the Alexander polynomial of a Lissajous knot is a square modulo 2 (it generalized the previous criterion of V.Jones) [51]. In the recent paper (with J.Kania Bartoszy´nska and Pat Gilmer), we have found the application of the Witten-Reshetikhin-Turaev invariants to study of symmetry of 3-dimensional manifolds [66].

I worked (with K.Murasugi) on determination of braid index of links. We developed some concepts in graph theory needed for our work (index of a graph) We conjectured that the braid index of an alternating link L is equal to the number of Seifert circles of an alternating diagram DL of L minus the index of DL,. We proved the conjecture for a large class of alternating links [37]. We found also examples of alternating links for which Morton-Franks-Williams inequalities do not become equalities (as in all previously known cases). In the actual computation (performed by J.Hoste) of the skein (Homflypt) polynomial we used ideas from [34] on the computational complexity of Jones type invariants.

4. tk-moves

I have been analyzing the so-called tk moves (k-twists) on links and the problem whether two links are equivalent by these moves, and if yes, how many moves are needed. The new

polynomial link invariants are the perfect tool to study these questions [16]. I also analyzed the behavior of the first homology group of branched cyclic covers under tk moves [16],[17]. I

obtained the nice corollary which relates the tricoloring of Fox and the Jones (and Kauffman) polynomials of links (at sixth root of unity) [35],[49].

5. Properties of Jones type polynomials

I have been analyzing diagrams for which Morton-Franks-Williams inequalities become equalities. I have proved (with K.Murasugi) that the coefficient in the highest power of z in the skein polynomial is multiplicative under planar star product [24].

6. Khovanov homology

Original Khovanov homology was defined (in 1997) for links in S3. We generalized the definition (with M.M.Asaeda and A.S.Sikora) to some other 3-dimensional manofolds (I bundles over surfaces). We showed also how to stratify Khovanov homology in order to categorify the Kauffman bracket skein module (in M = I˜×F case). I studied also (with M.M.Asaeda) torsion in Khovanov homology [A-P] proving Shumakowitch “torsion” conjecture for a class of adequate links. Recently (May 2005) I noticed the connection between Khovanov

homology and Hochschild homology. I am analyzing this connection and its consequences. In particular we use the connection to compute some Khovanov homology of links and graphs,

and analyze their torsion.

7. Algebraic topology of knots in 3-manifolds

(a) I tried to construct a “multilabel” Jones polynomial, with a partial success [21], but then I realized that the proper idea is to associate to each 3-manifold a module over the ring of

polynomials (I have called it skein module). The existence of the generalized Jones (skein) polynomial for S^{3}is equivalent to the fact that the third skein module of S^{3}(S_{3}(S^{3})) is

equal to the one generator free module. S3 is a well defined object but it is very difficult to compute. The only nontrivial results known before (after a proper interpretation) where

for S^{3}and S^{1}×D^{2}(Hoste and Kidwell, Turaev). I outlined the theory of skein modules in [28]. The skein module S^{3}(M) (respectively S_{2,∞}(M)) is a straightforward generalization

of the skein (Homfly) (resp. Jones) polynomial to any 3-manifolds. We have found (with J.Hoste) the (2,∞)-skein module of lens spaces. Namely we proved that S_{2,∞}(L(p, q)),

for p > 1 is a free Z[A±1] module with ⌊p 2 ⌋+1 generators (here ⌊x⌋ is the greatest integer function). Additionally we showed that S_{2,∞}(S^{1}× S^{2}) is infinitely generated but the

torsion free part of it is free on one generator [36]. We completed the computation of the S_{2,∞}(S^{1}×S^{2}) in [41]. I have analyzed (with J.Hoste) the structure of (2,∞)-skein module

of open contractible 3-manifolds. For an uncountable collection of open contractible 3-manifolds, each constructed in a fashion similar to that of the Whitehead manifold, we

prove that their (2,∞)-skein modules are infinitely generated, torsion free but not free. To each of these manifolds one may associate a subgroup G of the rationals which may

be interpreted via wrapping numbers (McMillan group). We show that the skein module has a natural filtration by modules indexed by G. These examples stand in stark contrast

to R^{3}, whose (2,∞)-skein module is free on one generator [40].

(b) I have proven that the skein module of the handlebody, S_{3}(H_{n}), is a free module with a natural basis, solving the conjecture by V.Turaev and myself (for D^{3}it is equivalent to the

existence of the skein (Homfly) polynomial and for S^{1}×D^{2}it has been solved by J.Hoste and M.Kidwell, and V.Turaev). The proof consists of a delicate multistep induction which

incorporates, in addition to ideas from knot theory, the method used in the classical proof of the Poincar´e-Birkhoff-Witt theorem on universal enveloping algebras of Lie algebras.

Of interest is also the structure of descending diagrams of links and description of S^{3}as a quantization of the “anti-homotopy” skein module (analyzed together with J.Hoste). I extended the above results to any closed surface cross interval using Hass, Scott and Grayson results on curvature flow on surfaces [31].

(c) I have proven that the skein module of links in F × I, S_{3}(F × I), where F is a planar surface, is a Hopf algebra (i.e. quantum group) with the standard multiplication (L_{1}L_{2 }means the link obtained by placing L_{1}above L_{2}in F × I), comultiplication of Jaeger- Turaev and antipode related to the mirror image. It settles a conjecture of V.Turaev [32].

(d) I analyzed the behavior of skein modules under connected sum and disc sum and found that in the case of a field of rational functions the skein module of connected sum is equal

to the tensor product of skein modules of factors. Generally (up to Poincare Conjecture) the skein module of the connected sum of 3-manifolds has a torsion. In the case of the

disc sum the behavior of skein modules reminds combinatorics of Topological Quantum Field Theories.

(e) I have investigated the skein module approach to Vassiliev-Gusarov invariants of knots and I have found, probably, the first concrete application of Vassiliev-Gusarov invariants (to knot’s periodicity) [38].

(f) The skein modules could play the role similar to homology or homotopy groups in algebraic topology. They can be thought as quantizations of the fundamental group or the first

homology group of a 3-manifold. Combinatorial methods were sufficient to compute S_{3}for S^{3}and the solid torus and S_{2,∞}, for I-bundles over surfaces and lens spaces. For more

computations some more sophisticated methods were needed: For example the Goldman-Wolpert Lie algebra build on homotopy classes of oriented closed curves, πˆ , on a surface

F and the Poincar´e-Birkhoff-Witt theorem gave a hint into the analysis of the third skein module of a handlebody S_{3}(H_{n}) (see [31]). I am working now on the Conjecture that

the third skein module (S_{3}) of an oriented, compact, irreducible, atoroidal 3-manifold is isomorphic to the symmetric tensor algebra of the module over conjugacy classes of

nontrivial elements of the fundamental group of the manifold. I proved it for F × I) [31] and it seems to hold also in the case of lens spaces [8p].

In recent papers (with A.Sikora) [50,55,11p] we introduced the concept of a skein algebra of a group (for a 3-manifold group, the Kauffman bracket skein module is a quantization

of the algebra). We started systematic study of algebras (and its relations with SL(2,C) character varieties) in particular proving that the minimal number of generators of the

free group Fd is equal to 2d − 1. We proved, for surface groups, the Bullock conjecture, that the skein algebra of F × I, for A = −1, is isomorphic to the coordinate ring of the

character variety of the fundamental group of the surface F. We found also the first nontrivial relation between Jones type invariants and hyperbolic structures on 3-manifolds.

In a recent work with D.Bullock [54], we have found the exact structure of the Kauffman bracket skein algebra of F ×I for surfaces with small Euler characteristic (including torus and a disk with 3 holes).

8. Positive and almost positive knots

In [24], I analyzed the signature of positive knots. Recently, with K. Taniyama, I generalized results from [24] and proved, for example, that [6p] - unknotting number 1 positive knots are twist knots, a knot with a diagram of no more than 2 negative crossings has negative signature or is a twist knot.

9. Computational complexity of Jones-type polynomialsI worked on relations between polynomials of knots and graphs [34]. In particular, I analyzed (with T. Przytycka) how much of Jones-type polynomials can be computed in subexponential time (generally computing Jones-type invariants is #P-hard) [34]. This work found many application when knots of several (> 35) crossings were considered. From perspective this work is important as it may be treated as a precursor of Vassiliev invariants (some truncations of Jones type invariants, considered in [34] are exactly Vassiliev parts of Jones type invariants).

10. Topological Graph Theory

I analyzed (with T.Przytycka) some problems of topological graph theory [26,33,44] solving in particular the problem of triangulations of surfaces without short noncontractible cycles.

I have analyzed completions of graph algebras which are Hopf algebras and are related to Vassiliev invariants of links [3p].

11. Incompressible surfaces

My PhD thesis was concentrated on incompressible surfaces in 3-manifolds, with the main result (from the perspective of 12 years): “Handle addition Lemma”. I would like to finish our

(with M.Lozano) classification of incompressible surfaces in the complements of closed 3-braids. I would like to find all Dehn fillings of punctured torus bundles over S1 which produce lens spaces, or more generally, Seifert manifolds. The idea is to use Thurston-Hatcher-Floyd method of finding incompressible surfaces, to, not necessarily incompressible, surfaces. Examples which will arise can be of interest for people generalizing “cyclic surgery theorem” and working on related topics. It would be also of interest to find an alternate proof of the classification of closed 3-braids (obtained by J.Birman and W.Menasco) using incompressible surfaces in 3-braid’s exterior. The structure of skein modules of 3-manifolds seems to be reflecting the geometric structure of these manifolds. For example one of the simplest skein modules is torsion free iff the manifold does not contain a nonseparating torus or a sphere. This seems to be leading to exciting research.

A brief description of proposed research.

My goal is to build an algebraic topology based on knots; that is a consistent theory in which links play the role of cycles, and skein modules the role of homology groups. Witten-Reshetikhin-Turaev-Wenzl invariants of 3-manifolds should correspond to some characteristic elements of cohomology groups. This is a far-reaching program. Until now we have been limited to 3-manifolds, with only a glance towards 4-manifolds, and our skein modules correspond to H_{1}of manifolds (often being a quantization of H_{1}). The situation is somehow reminiscent of that of “classical” algebraic topology 100 years ago (before Poincar´e’s fundamental paper “Analysis Situs”, 1895). At present we are able to compute a few isolated examples, but there are already signs that it will rise in future to a beautiful and powerful theory.

A personal statement about my research career to date and aspirations in the long-term.

My research concentrated on topology of low dimensional manifolds:

1. Cyclic actions on 2 and 3-manifolds.

This resulted in my Master Degree Thesis and in my constant interest in symmetry of manifolds (I have written a survey of methods applicable for symmetric links and 3-manifolds [52]).

2. Incompressible surfaces in 3-manifolds.

My main results are related to the “Handle addition Lemma”. This result, motivated by the question of when incompressibility of surfaces survives a Dehn surgery, unleashed a whole

industry which culminated in the proof of the R-conjecture (by Gabai) and the Tietze conjecture (by Gordon and Luecke). Scharlemann first tested his powerful technique on a generalization of my lemma.

3. 3-dimensional hyperbolic manifolds.

I worked intensively on the topic for a short time (1982) but my suggestion that the Thurston example (5/1 surgery on the figure eight knot) is not the 3-manifold of the smallest hyperbolic

volume was correct. I conjectured that the smallest volume hyperbolic 3-manifold is obtained by a surgery on the punctured torus bundle over S1 with monodromy being minus that of the

figure eight knot. This is still the example with the smallest volume. When working on knot theory in 3-manifolds I always have the Thurston geometrization conjecture in background.

4. Knot theory in 3-manifolds.

I was one of the co-inventors of generalized Jones polynomials and I analyzed several of their properties. However, I believe, my most important work was done in the theory of skein

modules of 3-manifolds. It is still restricted to examples but my result that the third skein module of a surface cross the unit interval is, on the one hand, a module isomorphic to the

symmetric tensor algebra over conjugacy classes of the fundamental group, and on the other hand has a structure of a non-commutative non-cocommutative Hopf algebra, seems to point

the way for future research.

5. Algebraic topology based on knots.

I imagine that this will relate to vast regions of mathematics including, besides the knot theory, geometric and algebraic topology, statistical mechanics, quantum groups and their representations, topological quantum field theory etc.

After traveling for 8 years and visiting several of the best mathematical centers (including Princeton and Berkeley), I would like here, at George Washington University, participate in the growth of a mathematical school in which “Algebraic topology based on knots” would be an important theme.

It would include:

1. Graduate students (I have/had already outstanding students (e.g. Adam Sikora, Maxim Sokolov, Tatsuya Tsukamoto, Qi Chen, Mietek D¸abkowski), and I am actively trying to recruit the best students in the world). I am talking to students at conferences, asking my friends mathematicians about possiblity of having their master students studying for PhD at GWU. Our newest (2005) students in PhD program were recruited in such a way. Radmila Sazdanovic gave (very good) talk at my conference Knots in Washington and Milena Pabiniak was recomended by her master degree advisor A. Pierzchalski, my friend from Lodz, Poland.

2. Research seminars, projects directed toward undergraduate students, writing textbooks (lecture notes prepared for my graduate course Topic Course in Topology will be a starting point for my planned book: Introduction to Algebraic Topology Based on Knots)

3. Organizing conferences (I co-organized eight special sessions at AMS meetings, I am co-organizing every semester a conference Knots in Washington; for example the one which took place in February 98 had about 40 participants (with J.Birman, T.Le and L. Feng as plenary speakers); the conference: KNOTS in WASHINGTON 10 Japan - USA ; workshop in Knot Theory, January 23-30, 2000, had about 35 speakers from 8 countries, including speakers from Japan, Korea, Russia, France, Italy, Slovenia and Colombia. Knots in Washington XVII; Khovanov Homology (May 2004) was supported by a grant from NSF. We had 5 plenary spekers – leading specialists in quickly emerging field of Khovanov

homology: M.Khovanov (he gave three talks), D.Bar-Natan, L.Rozanski, A.Shumakovitch and O.Viro. In November 2004, we organized Knots in Washington XIX: Topology in Biology, were recent ideas of applying knot theory to biology were discussed. Also February 2005 conference: Knots in Washington XX (60th birthday of Louis H. Kauffman) was an unqualified success with famous speakers (again including Khovanov and Viro and also Morton and Murasugi).

4. Informing the general public on mathematical activity.

I am open to collaboration with other people and I have written several joint papers e.g. with R.Anstee, M.M.Asaeda, S.Betley, D.Bullock, Q.Chen, M.A.Dabkowska, M.K.D¸abkowski, P.Gilmer, V.S.Harizanov, L.Helme-Guizon, J.Hoste, M.Ishiwata, W.Jakobsche, F.Jaeger, V.F.R.Jones, J.Kania-Bartoszy`nska, S.Lambropoulou,M.Lozano, W.J.R.Mitchell, K.Murasugi, M.Niebrzydowski, M.D.Pabiniak, T.M.Przytycka, D.Repovs, D.Rolfsen, Y.Rong,W.Rosicki, R.Sazdanovic, A.S.Sikora, D.Silver, M.Sokolov,

K.Taniyama, A.A.Togha, T.Tsukamoto, P.Traczyk, M.A.Veve, S.Williams, X.Zhu, A.Yasuhara and T.˙Zukowski.