Yongwu Rong  

Professor of Mathematics

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Yongwu Rong

 

Department of Mathematics

The George Washington University

Washington, D. C. 20052

U. S. A.

(202) 994-6890, (202)994-6760 (fax)

rong@gwu.edu

http://home.gwu.edu/~rong

 

Education

 

·        Ph.D. University of Texas at Austin, Mathematics, Advisor: Cameron McA. Gordon, 1989.

 

·        B.S. The University of Science Technology of China,  1983.

 

Professional Appointments

 

·        The George Washington University (1992 – present). Faculty.

Professor (2006- ).

·        National Science Foundation (2001-2003, and 2006). Program Director in DMS.

·        Institute for Advanced Study, Princeton (1999). Member.

·        Michigan State University (1989 – 1992). Research Postdoctor.

·        University of Texas at Austin (1990). Research visitor.

 

 

Research Publications.

 

·        A generalization of Hadamard's determinantal inequality, with Z. Shen,  J. China Univ. Sci. Tech. Math. Issue, 13 (1983) 272-274.

·        Continuous linear functionals on the F-space , J. China Univ. Sci. Tech.  14 (1984) 166-169.

·        The Kauffman polynomial and the two-fold cover of a link, Indiana Univ. Math. Journ.  Vol. 40 No. 1 (1991) 321-331.

·         Degree one maps between geometric three-manifolds, Trans. Amer. Math. Soc.   Vol.  {\bf 332}  No. 1, (1992) 411-436.

·        The preimages of submanifolds, with S. Wang, Mathematical  Proceedings of the Cambridge Philosophical  Society.  112  (1992) 271 - 279.

·        Maps between Seifert fibered spaces of infinite , Pacific Journal of Mathematics,  Vol. 160 No. 1 (1993) 143-154.

·        Some knots not determined by their complements, Quantum Topology,  Series of Knots and Everything, Vol. 3, edited by L. Kauffman and R. Baadhio. (1993) 339-353.

·        Mutation and Witten invariants, Topology, Vol. 33, No. 3 (1994) 499-507.

·        Degree one maps of Seifert manifolds and a note on Seifert Volume, Topology and Its Applications, 64 (1995) 191-200.

·        Link Polynomials of higher order, Journ. London Math. Soc. (2) 56 (1997) 189-208.

·        On derivatives of link polynomials,  with W. B. R. Lickorish, Topology and Its Applications, 87 (1998) 63-71.

·        Approximating Jones coefficients and other link invariants by Vassiliev invariants, with I. Kofman,  Journ. Knot Theory and Its Ramifications, Vol. 9, No. 7 (2000) 955-966.

·        Vassiliev invariants from satellites of link polynomials, with M. McDaniel,  Kobe Journal of Mathematics, 18 (2001) 127-145.

·         Linear independence of derivatives of link polynomials, Topology and Its Applications, 117 (2002) 191-198.

·        A categorification for the chromatic polynomial, with L. Helme-Guizon,  Algebraic and Geometric Topology (2005) 1365-1388.

·        Torsions in graph cohomology, with L. Helme-Guizon and J. Przytycki,  Fundamenta Mathematicae, 190 (2006) 139-177.

·        Examples of Knots with the Same Polynomials, with K. Luse, Journ. Knot Theory and Its Ramifications, 15 (2006) 749-759.

·        Knight moves for chromatic graph homology, with M. Chmutov and S. Chmutov, accepted for publication by European Journal of Combinatorics. http://www.arxiv.org/abs/math.CO/0511598

·        A categorification for the Tutte polynomial, with F. Jasso-Hernandez,  Algebraic and Geometric Topology,  6 (2006) 2031-2049.

 

Grants

 

     Research Grants

 

·        Homological Algebra Methods in Topology and Combinatorics, Principle Investigator, National Science Foundation, DMS-0513918, $108,000. 2005-2008.

·        Knots in Washington XXI: Skein Modules, Khovanov Homology and Hochschild Homology. Co-PI with Jozef Przytycki and Alexnader Shumakovitch. National Science Foundation grant, DMS-0555648, $20,000. 2005-2006.

·        Quantum Computing and Jones Polynomials of Knots, GWU University Facilitating Fund,

      $7,931, 2001-2002.

·        Distinguishing Knots Using Jones Invariants, GWU Junior Scholar Incentive Award, GWU, $5,000, 1995 1996.

·        Jones-Witten Invariants of Knots, Principle Investigator, GWU University Facilitating Fund, $8,720, 1994-1995.

 

     Involvement with other grants (as a PI, co-PI, or a participant)

 

·        Co-organizer (with Jozef Przytycki) for the conference on ``Knots in Washington XVIII; Khovanov homology" in May 2004. This conference was supported by NSF grant, DMS-0432284.

·        PI for a special NSF grant for my IPA appointment at NSF during 2001-2003.

·        Participant for NSF institute award DMS-9729992 (awarded to IAS) during 1999.

·        Participant (with Joe Bonin, Rodica Simion, and Dan Ullman) for a FIPSE award from the Department of Education (awarded to Moravian College) on implementation of the new course ``Calculus with Precalculus" at GWU during 1995-1997.

 

 

 

Selected Invited Research Talks

 

·        Degree one maps between geometric 3-manifolds, AMS meeting - Special session on Low Dimensional Topology and  Combinatorial Groups, Portland, Oregon,  June 1991.

·        Gromov's norm of three-manifolds, seminar talk, University of Michigan, December 1991.

·        Three-Manifolds with the same Witten invariants, Midwest Geometry Conference, May 1993.

·        Links polynomials and Vassiliev Invariants, Summer workshop in low dimensional topology, Peking University, Beijing, China, June, 1994.

·        Examples of Mutative 3-Manifolds, Seventh Lehigh University Geometry and Topology Conference, Lehigh University, June 1995.

·        Cablings of Vassiliev invariants, invited seminar talk, Columbia University, October 1996.

·        Vassiliev invariants coming from link polynomials, Chinese University of Hong Kong, November 1997.

·        Degree one maps between 3-manifolds, invited colloquium, Peking University, Beijing, China, April 1999.

·        Quantum invariants in dimension three, invited olloquium, University of Science & Technology of China, Hefei, China, April 1999.

·        On higher order link polynomials, Japan-US joint conference Knots in Washington, Washington, DC, January 2000.

·        Subspaces in the space of Vassiliev invariants, Knots in Montreal Conference, Montreal, Canada, April 2001.

·        Constructing Links with the same polynomial, a series of four lectures given at the International Workshop on Low Dimensional Topology, Harbin, China, July 2001.

·        Approximating knot invariants by Vassiliev invariants, AMS meeting - special session on Quantum Topology in Dimension Three, Ann Arbor, Michigan, March 2002.

·        A Kauffman bracket type polynomial for Legendrian links, Knots in Washington Conference, Washington, DC, December 2003.

·        A Khovanov type homology theory for graphs. AMS meeting - special session on Knot Theory and Its Applications, Tallahassee, Florida, March 2004.

·        Homological Algebra Methods in Graph Theory, Mathematics Colloquium, University of South Florida, Tampa, Florida, March 2005.

·        Homological Algebra methods in graph theory. Post-conference talk at the Conference on 3-Manifolds and Knot Theory, in honor of 60th birthday for Professor Cameron Gordon. Austin, Texas, May 2005.

·        A quadruply-graded graph homology for the Bollobas-Riordan polynomial, Knots in Washington XXI: Skein modules, Khovanov homology and Hochschild homology, Washington, DC, December, 2005.

·        Khovanov type homology theories for graphs, International Conference Categofications in Algebra and Topology 2006, Uppsala, Sweden, September 2006.

·        Homological algebra methods in graph theory, Colloquium, University of Oklahoma, Norman, OK, October 2006.

·        Categorifications in graph theory, Colloquium, Oklahoma State University, Stillwater, OK, October 2006.

 

 

Ph.D. students

 

     Previous Ph.D. students:

·        Michael E.\  McDaniel, Subspaces of Vassiliev invariants using cabling, 1997.

·        Laure Helme-Guizon, A categorification of the chromatic polynomial, 2005.

 

     Current Ph.D. students:

·        E. Fanny Jasso-Hernandez, expect to graduate in 2007.

·        Kerry Luse, expect to graduate in 2008.

 

Other mentorees:

·        Ilya Kofman (2000 Ph.D. from University of Maryland at College Park under Bill Goldman).

      Dissertation title: Vassiliev invariants of knots and links in $S^3$ and other 3-manifolds.

·        Senior Thesis Advisor for Amy L. Nagahashi, Billiard Links in the 3-Ball, 2001.

 

Selected Services

 

·        Deputy Chair, Mathematics Department, Fall 2005.

·        GWU Science Building Working Committee, 2006.

·        Chair for the Search Committee in Topology, 2004-2005.

·        Chair for the Undergraduate Committee, 2003-2004.

·        Search Committee in various years.

·        AMS annual meeting Committee on Local Arrangements, 2000.

·        Colloquium Organizer and E \& R fund coordinator, 1994-1996.

·        Reviewer for the Mathematical Reviews of AMS, Zentralblatt Math of the European Mathematical Society, and the National Science Foundation.

·        Referee for dozens of mathematical journals.

·        Organizer and co-organizer for several AMS special sessions.

·        Co-founder (with Jozef Przytycki) and co-organizer (with various people) for the Knots in Washington Conference.