**GWU Topology Seminar, Fall
2007**

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

Speaker: Maciek
Mroczkowski (

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

Title: Khovanov homology of
framed and signed chord diagrams

Place: Monroe Hall,

**October 5, 2007, Friday; 1:00 – 2:00pm**

Speaker: John Armstrong,

Title: Categorification of Quandle Coloring Numbers by Anafunctors*
(abstract below)

Place: Monroe Hall,

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

Speaker: Alexander Shumakovitch,

Title: Rasmussen invariant
and sliceness of knots * (abstract below)

Place: Monroe Hall,

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

Speaker: Hao
Wu,

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,

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

Speaker: Milena
Pabiniak,

Abstract: see below.

Place: Monroe Hall,

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

Speakers: Dan Silver and
Susan Williams,

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

Place: Monroe Hall,

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

Speakers: Radmila Sazdanovic, GWU.

Title: Torsion in Khovanov
homology of semi-adequate links

Place: Monroe Hall,

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

Speakers: Dan Silver and
Susan Williams,

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

Place: Monroe Hall,

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

Speakers: Dan Silver and
Susan Williams,

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

Place: Monroe Hall,

**KNOTS IN **

**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