Other area seminars. Our e-mail list. Archive of previous semesters
Columbia Geometric Topology SeminarFall 2023 |
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Organizers: Ross Akhmechet, Siddhi Krishna, Francesco Lin
The GT seminar typically meets on Fridays at 2:00pm Eastern time in Room 307, Mathematics Department, Columbia University. It will also be live-streamed over Zoom.
Other area seminars. Our e-mail list. Archive of previous semesters
| Date | Time (Eastern) | Speaker | Title |
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September 8 |
2pm Eastern |
Liam Watson |
Khovanov multicurves are linear |
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September 15 |
2pm Eastern |
Faces of the Thurston norm ball dynamically represented by multiple distinct flows |
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September 22 |
2pm Eastern | Matt Hogancamp |
Khovanov homology and handleslides |
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September 29 |
2pm Eastern |
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October 6 |
2pm Eastern |
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October 13 |
2pm Eastern |
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October 20 |
2:10pm Eastern (note different time) |
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October 27 |
2pm Eastern | ||
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November 3 |
2pm Eastern |
Christine Lee |
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November 10 |
2pm Eastern (double header pt 1) |
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November 10 |
4pm Eastern (double header pt 2) |
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| November 17 |
2pm Eastern |
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December 1 |
2pm Eastern |
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December 8 |
2pm Eastern |
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Name: Liam Watson
Title: Khovanov multicurves are linear
Abstract: For a given invariant the geography problem asks for a characterization of values the invariant attains. For example, it is well understood which Laurent polynomials arise as the Alexander polynomial of a knot. By contrast, very little is known about which values the Jones polynomial takes. And the situation is at least as bad for Khovanov homology. So it is a little surprising that the Khovanov homology of a tangle, which can be framed in terms of immersed curves in the 4-punctured sphere, satisfies rather strict geography—the invariants are “linear”. My talk, which is based on joint work with Artem Kotelskiy and Claudius Zibrowius, will explain what “linear” means, and tell part of the story of how this comes up.
Name: Anna Parlak
Title: Faces of the Thurston norm ball dynamically represented by multiple distinct flows
Abstract: A pseudo-Anosov flow on a closed 3-manifold dynamically represents a face F of the Thurston norm ball if the cone on F is dual to the cone spanned by homology classes of closed orbits of the flow. Fried showed that for every fibered face of the Thurston norm ball there is a unique, up to isotopy and reparameterization, flow which dynamically represents the face. Mosher found sufficient conditions on a non-circular flow to dynamically represent a non-fibered face, but the problem of the existence and uniqueness of the flow for every non-fibered face was unresolved. I will outline how to show that a non-fibered face can be in fact dynamically represented by multiple topologically inequivalent flows, and discuss how two distinct flows representing the same face may be related.
Name: Matt Hogancamp
Title: Khovanov homology and handleslides
Abstract: If K is a framed knot and X is a link in the solid torus, then the satellite operation produces a link K(X), obtained by embedding X (the "pattern") into a tubular neighborhood of K (the "companion"). In the context of Khovanov homology, the patterns can be thought of as objects of a category called the annular Bar-Natan category (ABN), and the satellite operation defines a functor from ABN to bigraded vector spaces, sending a pattern X to Kh(K(X)). In this talk I will discuss joint work with Dave Rose and Paul Wedrich, in which we construct an object Ω (which we call a "Kirby color") in ABN such that Kh(K(Ω)) is invariant under handleslides. As I will explain, the object Ω encodes the Manolescu-Neithalath 2-handle formula for the sl(2) skein lasagna modules (which was inspirational for our work). Time permitting, I will discuss an intriguing description of the Kirby object in terms of some special braids (positive braid lifts of n-cycles) that we speculate may be more amenable for computation.