GWU Topology Seminar
Fall 2008 – Spring 2009
January 12 , 2009, Monday, 3:00 – 4:00 pm.
Speaker: David Penneys,
UC-Berkeley.
Title: Examples of planar algebras
Place: Monroe Hall,
February 20 , 2009, Friday, 4:15 - 5:15pm.
Speaker: Kouki Taniyama
(
Title: Circle immersions that can be divided into two arc
embeddings
Place: Monroe Hall,
Abstract:
We give a complete
characterization of a circle immersion that can be divided
into two arc embeddings in terms of its chord diagram.
Paper reference: http://arXiv.org/abs/0902.1478
March 6
, 2009, Friday, 4:15 - 5:15pm.
Speaker: Hao Wu,
Title: Khovanov-Rozansky homology
via matrix factorizations, part 1.
Place: Monroe Hall,
Abstract:
This is the first of a
series of talks aimed to give a detailed introduction to the Khovanov-Rozansky homology.
Friday, March 13, 4:15 - 5:15pm.
Speaker: Hao Wu,
Title: Khovanov-Rozansky homology via matrix factorizations, part
2.
Place: Monroe Hall, 2115 G Street, Room 267
Abstract:
This is the second of a series of talks aimed to give a detailed introduction
to the Khovanov-Rozansky homology.
Friday, March 27, 4:15-5:15pm.
Speaker: Hao Wu,
Title: Khovanov-Rozansky homology via matrix factorizations, part 3.
Place: Monroe Hall,
Friday, April 3, 4:15-5:15pm.
Speaker: Hao Wu,
Title: Khovanov-Rozansky homology via matrix factorizations, part 4.
Place: Monroe Hall,
Abstract: This is the fourth of a series of talks aimed to give a detailed introduction to the Khovanov-Rozansky homology. In this talk, I will define MOY graphs and the matrix factorizations associated to them. If time allows, I will prove the decomposition theorems.
And more talks by Hao Wu on Friday 4:15 – 5:15pm.
Friday, April 24, 4:15-5:15pm.
Speaker: Dragomir
Saric (
Title: The mapping class group cannot be realized by homeomorphisms
Place: Monroe Hall,
Abstract:
The mapping class group MCG(S) of a
closed surface S of genus at least 2 is quotient of the group of homeomorphisms
Homeo(S) by the subgroup Homeo_0(S) of homeomorphisms
homotopic to the identity. We show that MCG(S) does
not homeomorphically lift to Homeo(S)
which answers a question of Nielsen.
This is a joint work with V. Markovic.
Monday, April 27, 4 -5 pm.
Speaker: Alexander Shumakovitch,
Title: Homologically Z_2-thin knots have no 4-torsion in Khovanov homology.
Place: Monroe Hall,
Abstract: I will show how to use the Bockstein spectral sequence to prove that homologically Z_2-thin knots have no 4-torsion in Khovanov homology. This completes the proof of the fact that the integer Khovanov homology of alternating knots is completely determined by their Jones polynomial and signature.
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Seminar Talks in Fall 2008
Speaker: Witek Rosicki (
Title: Quandle Cocycle Invariants for Knots, Knotted Surfaces
and Knotted 3-Manifolds
Place: Monroe Hall,
Abstract:
A quandle is a non-associative algebraic structure. Carter, Jeslovsky, Kamada,
Langford and Saito (1999, 2003) constructed the quandle cohomology theory.
They found invariants of knots and knotted surfaces in 2-nd and 3-rd
quandle cohomology. Similar invariants exists for knotted
3-manifolds in 5-sphere in 4-th quandle cohomology.
Speaker: Krzysztof Putyra (
Title: Cobordisms with chronology
Place: Monroe Hall,
Abstract:
I will enrich cobordisms with special projections on the closed interval I = [0; 1]
to break the symmetry of oriented cobordisms. This creates a new category, which in case
of dimension two has a nice presentation by generators and relations. This category
can be used to give a functorial description of the construction of odd link homology as
well as to define a new type of TQFT's.
Speaker: Krzysztof Putyra (
Title: Odd link homology theories given by chronological TQFT's
Place: Monroe Hall,
Abstract:
For a given tangle diagram T I will build the Khovanov complex Kh(T) in the category of cobordisms with chronology.
It is invariant under Reidemeister moves up to chain homotopies, relations analogous to Bar-Natan's S/T/4Tu
and a condition given by a chronology change. Any chronological TQFT satisfying these additional conditions
defines a complex in the category of modules and we can compute its homology. This procedure generalises
both Khovanov and odd link homology theories.
Speaker: Melissa Macasieb,
Title: Character Varieties of an Infinite Family of Two-Bridge Knots
Place: Monroe Hall,
Abstract:
To every hyperbolic finite volume 3-manifold M, one can associate a pair
of related algebraic varieties X(M) and Y(M), the SL_2(C)- and
PSL_2(C)-character varieties of M. These varieties carry much
topological information about M, but are in general difficult to
compute. If M has one cusp, then both these varieties have dimension
one. In this talk, I will also show how to obtain explicit equations for
the character varieties associated to a family of hyperbolic two-bridge
knot complements S^3-K(m,n) and discuss some interesting consequences of
this work.
This is joint work with Kate Petersen and Ronald van Luijk.
Speaker:
Title: Introduction to group actions on generalized complex manifolds
Place: Monroe Hall,
Abstract:
Generalized complex geometry was introduced by Hitchin and further developed by his students.
It is a simultaneous generalization of both symplectic geometry and complex geometry and so
is well-suited to the study of things related to both, e.g., Mirror symmetry. In this talk, we will
review the notions of generalized moment map, Hamiltonian action and quotient in generalized
complex geometry. Then we will explain the Morse-Bott theory behind the geometry of
generalized moment maps. We explain that central results in Hamiltonian symplectic geometry,
such as the Duistermaat-Heckman theorem, equivariant formality, and Kirwan injectivity and
surjectivity extend to Hamiltonian actions on generalized complex manifolds.
November 13, Thursday,
2008,
Speaker: Ivan Dynnikov,
Title: A geometric approach to braid conjugacy.
Place:
Abstract:
I will speak about an algorithm that is conjectured to solve the
conjugator search problem for braids in polynomial time. It is based on
geometric presentation of braids as homeomorphisms of a punctured disk
rather than algebraic one.
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Some Previous Topology Seminars: