GWU Topology Seminar, Fall 2007

 

 

September 13, Thursday. 2:45 3:45pm

Speaker: Maciek Mroczkowski (Gdansk University)

Title: Homflypt and Kauffman skein modules of twisted I bundles of unoriented surfaces

Place: GWU, Mathematics Department, Monroe Hall, Seminar Room

Contact person: Jozef Przytycki (przytyck@gwu.edu)

 

September 29, 2007, Saturday;  1:00 2:00pm

Speaker: Oleg Viro (Stony Brook and St. Petersburg Branch of Mathematical Institute of Russian Academy of Sciences)

Title: Khovanov homology of framed and signed chord diagrams

Place: Monroe Hall, 2115 G Street, Room 267  

 

October 5, 2007, Friday;  1:00 2:00pm

Speaker: John Armstrong, Tulane University 

Title: Categorification of Quandle Coloring Numbers by Anafunctors* (abstract below)
Place: Monroe Hall, 2115 G Street, Room 267  

 

October 25, 2007, Thursday;  11:10 am.

Speaker: Alexander Shumakovitch, George Washington University

Title: Rasmussen invariant and sliceness of knots * (abstract below)
Place: Monroe Hall, 2115 G Street, Room 267  


November 15, 2007, Thursday;  11:10 12:25.

Speaker: Hao Wu, George Washington University

Title: Bennequin inequalities from the Khovanov-Rozansky homology (a.k.a. How to play Alex's game for n>2)* (abstract below)
Place: Monroe Hall, 2115 G Street, Room 267  

 

November 16, 2007, Friday, 12:45 - 2:00.

Speaker: Milena Pabiniak, George Washington University

Abstract: see below.

Place: Monroe Hall, 2115 G Street, Room 267  

 

November 28, 2007, Wednesday, 2:20 3:35.

Speakers: Dan Silver and Susan Williams, University of South Alabama

Title: On applications of Dynamical systems to Knot Theory I - Introduction

Place: Monroe Hall, 2115 G Street, Room 267  

 

November 30, 2007, Friday, 12:45 - 2:00

Speakers: Radmila Sazdanovic, GWU.

Title: Torsion in Khovanov homology of semi-adequate links

Place: Monroe Hall, 2115 G Street, Room 267  

 

December 5, 2007, Wednesday, 3:45 - 5:00

Speakers: Dan Silver and Susan Williams, University of South Alabama

Title: On applications of Dynamical systems to Knot Theory II - Algebraic dynamics

Place: Monroe Hall, 2115 G Street, Room B03.

December 6, 2007, Thursday, 11:10 12:25

Speakers: Dan Silver and Susan Williams, University of South Alabama

Title: On applications of Dynamical systems to Knot Theory III - Twisting

Place: Monroe Hall, 2115 G Street, Room 267  

 

KNOTS IN WASHINGTON XXV - Dedicated to Herbert Seifert on his 100 birthday

The 25th Conference on Knot Theory and its Ramifications

December 7-9, 2007

 

http://home.gwu.edu/~przytyck/knots/knotsinwashington25.htm

 

The conference will start at 1.30 PM on Friday, December 7th at the MPA building Room 310

with the Colloquium type talk:

Speakers: Dan Silver and Susan Williams

Title: From Nuts to Knots: An irreverent look at the origins of Knot Theory

 

 ==============================================================================

 

ABSTRACTS OF TALKS

 

October 5, 2007, John Armstrong, Categorification of Quandle Coloring Numbers by Anafunctors

 

The number of colorings of a link by a given quandle is a classical
invariant of links up to ambient isotopy. We would like to categorify
and extend this invariant to the category $\mathcal{T}ang$ of tangles.
Here, we show how to associate, functorially, to each tangle an
anafunctor between two comma categories of quandles. When we restrict
this assignment to knots and links and specify a quandle $Q$ of
colors we recover $Q$-coloring invariant. If we first decategorify
and specify a quandle $Q$ of colors we recover the $Q$-coloring
matrix of a given tangle.

 

October 25, 2007, Alexander Shumakovitch, Rasmussen invariant and sliceness of knots

 

 We use Rasmussen invariant to find knots that are topologically
 locally-flatly slice but not smoothly slice. We also note that this
 invariant can be used to give a combinatorial proof of the
 slice-Bennequin inequality for links. Finally, we compute the Rasmussen
 invariant for quasipositive knots and show that most of our examples of
 non-slice knots are not quasipositive and were to the best of our knowledge
 unknown before.

 

November 15, 2007, Hao Wu, Bennequin inequalities from the Khovanov-Rozansky homology (a.k.a. How to play Alex's game for n>2)

 

This talk is a continuation of Alex's recent talk. I will explain three things.

(i) How to establish a strong Bennequin type inequality using the Khovanov-Rozansky homology.

(ii) How to generalize the Rasmussen invariant and the Alex-Olga inequality.

(iii) How to generalize Olga's invariant for transversal links. I will also talk about relations between these objects.

 

 

November 16, 2007, Milena Pabiniak.

 

Skein modules were defined by J.H.Przytycki to generalize various skein relations of polynomial

invariants in S^3 to arbitrary 3-manifolds. Soon it was noticed that for some class of manifolds,

trivial I-bundles, Fx I, over orientable surface F, one can easily obtain an algebra, not only module,

structure. We will start with definition and basic properties of Kauffman Bracket Skein Module, present

results for few basic 3-manifolds and examples of algebra structures for I-bundles. Then we will

concentrate on twisted I -bundles. Our goal was to define a structure of algebra or similar to algebra for

skein module of twisted I-bundles over non orientable surfaces F. It appears that for simple non-orientable

surfaces we can still define commutative algebra structure

Previous Topology Seminars