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September 7
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Tom Mark (UVa)
Title: A survey of applications of Heegaard Floer homology
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September 14
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Matthew Hogancamp (UVa)
Title: Matrix Factorizations and an application to link homology
We will discuss the need for a new procedure in the categorification of the SL(N) specializations of the Homfly polynomial for oriented links. Matrix factorizations will be introduced, and the construction of Khovanov-Rozansky homology using them using them will be described.
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September 22*
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Olga Plamenevskaya (SUNY Stony Brook)
(Special time: Tuesday 2-3pm)
Title: Lens spaces, Legendrian surgeries and symplectic fillings
Classical theorems in low-dimensional topology assert that
every smooth 3-manifold bounds a 4-manifold, and any two 3-manifolds
can be obtained from one another by a surgery on a link.
In the world of contact topology, Legendrian surgeries between
contact 3-manifolds are harder to find; not every contact
3-manifold bounds a symplectic 4-manifold.
We will provide some background, survey the classical results,
and discuss classification of symplectic fillings for all tight
contact structures on L(p,1), as well as some results on Legendrian
surgeries between lens spaces. Part of this work is joint with Jeremy
Van Horn-Morris.
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September 28
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No seminar. Regulars are encouraged to attend the topology seminar this week, where Robert Lipshitz (Columbia University) will give a geometry-influenced talk.
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October 6
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Reading holiday
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October 12 |
Roland van der Veen (University of Amsterdam)
Title:The volume conjecture for knotted graphs
The volume conjecture proposes to relate the Jones polynomial of a knot to the geometry of its complement.
More specifically certain evaluations of the colored Jones polynomial should converge to the hyperbolic volume of the knot.
We propose to extend the volume conjecture to knotted graphs and show that it holds true for a large family of such graphs.
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October 19
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October 26
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Sean Droms (UVa)
Title: Heegaard Floer homology detects the Thurston norm
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November 2
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Stanislav Jabuka (University of Nevada, Reno)
Title: Applications of Witt rings in knot theory
Given a field F, the Witt ring W(F) is the set of equivalence classes of symmetric, bilinear, non-degenerate forms on finite dimensional F-vector spaces. The equivalence relation among such forms is generated by the presence of metabolizers while the ring operations are those of direct sums and tensor products.
After reviewing the construction and some basic properties of Witt rings, especially for the case of F being the rational numbers, I shall explain how Witt rings can be used to define invariants of knots. As an application of these invariants, I will discuss unknotting numbers of knots and sliceness obstructions for knots.
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November 9
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No seminar
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November 16
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Slava Krushkal (UVa)
Title: Topological arbiters
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November 20*
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Lawrence Roberts (University of Alabama)
(Special Friday seminar, 3:30pm in Kerchof 326)
Title: Finding bounds for the Oszvath-Szabo tau invariant of a satellite knot
For a knot K, τ(K) is a concordance invariant which gives a lower
bound on the genus of any surface in the four ball with boundary K. Recently, there
have been some results giving bounds, and computations, for τ(K) when K is a
cabled knot. I will describe a different technique which provides weaker bounds, but
works for almost all satellites. I will first describe the properties of the τ-invariant
and give some idea of its construction, and then describe my approach. While this invariant
arises from Heegaard-Floer homology, no knowledge of the techniques of Floer homology is required.
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November 23
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Novmeber 30
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Ben Cooper (UVa)
Title: TBA
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December 7
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Hao Wu (George Washington University)
Title: A colored sl(N)-homology for links in S3
I will introduce an sl(N)-homology for links colored by wedge powers of the defining representation, which generalizes the sl(N)-Khovanov-Rozansky homology. The construction is based on matrix factorizations over rings of symmetric polynomials associated to MOY graphs. I believe this homology categorifies the corresponding Reshetikhin-Turaev invariant.
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