### TBA by Chris Leininger

- Series
- Geometry Topology Seminar
- Time
- Monday, October 23, 2023 - 14:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Chris Leininger – Rice University

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- Series
- Geometry Topology Seminar
- Time
- Monday, October 23, 2023 - 14:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Chris Leininger – Rice University

- Series
- Geometry Topology Seminar
- Time
- Monday, August 28, 2023 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Vitalijs Brejevs – University of Vienna – brejka@gmail.com

- Series
- Geometry Topology Seminar
- Time
- Monday, May 1, 2023 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Farid Diaf – Université Grenoble Alpes – diaffarid97@gmail.com

In 1990, Mess gave a proof of Thurston's earthquake theorem using the Anti-de Sitter geometry. Since then, several of Mess's ideas have been used to investigate the correspondence between surfaces in 3-dimensional Anti de Sitter space and Teichmüller theory.

In this spirit, we investigate the problem of the existence of vector fields giving infinitesimal earthquakes on the hyperbolic plane, using the so-called Half-pipe geometry which is the dual of Minkowski geometry in a suitable sense. In particular, we recover Gardiner's theorem, which states that any Zygmund vector field on the circle can be represented as an infinitesimal earthquake. Our findings suggest a connection between vector fields on the hyperbolic plane and surfaces in 3-dimensional Half-pipe space, which may be suggestive of a bigger picture.

- Series
- Geometry Topology Seminar
- Time
- Monday, April 24, 2023 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Francis Bonahon – University of Southern California – fbonahon@usc.edu

**Please Note:** There will be a pretalk 1-1:40pm in Skiles 006.

This talk is motivated by surprising connections between two very different approaches to 3-dimensional topology, and more precisely by the Kashaev-Murakami-Murakami Volume Conjecture, which relates the growth of colored Jones polynomials of a knot to the hyperbolic volume of its complement. I will discuss a closely related conjecture for diffeomorphisms of surfaces, based on the representation theory of the Kauffman bracket skein algebra of the surface, a quantum topology object closely related to the Jones polynomial of a knot. I will describe partial results obtained in joint work with Helen Wong and Tian Yang.

- Series
- Geometry Topology Seminar
- Time
- Monday, April 17, 2023 - 16:30 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Peter Lambert-Cole – University of Georgia

This talk will have two parts. The first half will describe how to construct symplectic structures on trisected 4-manifolds. This construction is inspired by projective complex geometry and completely characterizes symplectic 4-manifolds among all smooth 4-manifolds. The second half will address a curious phenomenon: symplectic 4-manifolds appear to not admit any interesting connected sum decompositions. One potential explanation is that every embedded 3-sphere can be made contact-type. I will outline some strategies to prove this from a trisections perspective, describe some of the obstructions, and give evidence that these obstructions may be overcome.

- Series
- Geometry Topology Seminar
- Time
- Monday, April 17, 2023 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Speaker
- Effie Kalfagianni – Michigan State University – kalfagia@msu.edu

It has been long known that the quadratic term in the degree of the colored Jones polynomial of knot provides a lower bound of the crossing number the knot.

I’ll discuss work with Lee where we determine the class of knots for which this bound is sharp and give applications to computing crossing numbers of satellite knots.

- Series
- Geometry Topology Seminar
- Time
- Monday, April 10, 2023 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Adam Sikora – SUNY Buffalo – asikora@buffalo

The Kauffman bracket skein module S(M) of a 3-manifold M classifies polynomial invariants of links in M satisfying Kauffman bracket skein relations. Witten conjectured that the skein module (over a field, with generic A) is finite dimensional for any closed 3-manifold M. This conjecture was proved by Gunningham, Jordan, and Safronov, however their work does not lead to an explicit computation of S(M).

In fact, S(M) has been computed for a few specific families of closed 3-manifolds so far. We introduce a novel method of computing these skein modules for certain rational homology spheres. (This is joint work with R. Detcherry and E. Kalfagianni.)

- Series
- Geometry Topology Seminar
- Time
- Monday, April 3, 2023 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Agniva Roy – Georgia Tech – aroy86@gatech.edu

In high dimensional contact and symplectic topology, finding interesting constructions for Legendrian submanifolds is an active area of research. Further, it is desirable that the constructions lend themselves nicely to computation of invariants. The doubling construction was defined by Ekholm, which uses Lagrangian fillings of a Legendrian knot in standard contact R^{2n-1} to produce a closed Legendrian submanifold in standard contact R^{2n+1}. Later Courte-Ekholm showed that symmetric doubles of embedded fillings are "uninteresting". In recent work the symmetric doubling construction was generalised to any contact manifold, giving two isotopic constructions related to open book decompositions of the ambient manifold. In a separate joint work with James Hughes, we explore the asymmetric doubling construction through Legendrian weaves.

- Series
- Geometry Topology Seminar
- Time
- Monday, March 27, 2023 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Anup Poudel – Ohio State – poudel.33@osu.edu

In this talk, we will explore and make comparisons between various models that exist for spherical tensor categories associated to the category of representations of the quantum group U_q(SL_n). In particular, we will discuss the combinatorial model of Murakami-Ohtsuki-Yamada (MOY), the n-valent ribbon model of Sikora and the trivalent spider category of Cautis-Kamnitzer-Morrison (CKM). We conclude by showing that the full subcategory of the spider category from CKM, whose objects are monoidally generated by the standard representation and its dual, is equivalent as a spherical braided category to Sikora's quotient category. This proves a conjecture of Le and Sikora and also answers a question from Morrison's Ph.D. thesis.

- Series
- Geometry Topology Seminar
- Time
- Monday, March 20, 2023 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Speaker