Other area seminars. Our e-mail list. Archive of previous semesters
Columbia Geometric Topology SeminarFall 2024 |
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Organizers: Ross Akhmechet, Deeparaj Bhat, Siddhi Krishna, Francesco Lin
The GT seminar typically meets on Fridays at 2:00pm Eastern time in Room 407, Mathematics Department, Columbia University.
Other area seminars. Our e-mail list. Archive of previous semesters
| Date | Time (Eastern) | Speaker | Title |
|---|---|---|---|
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September 13 |
2pm |
Ben Lowe (UChicago) |
Rigidity and Finiteness of Totally Geodesic Hypersurfaces in Negative Curvature |
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September 20 |
2pm | Qiuyu Ren (UC Berkeley) |
Lasagna s-invariant detects exotic 4-manifolds |
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September 27 |
2pm |
John Baldwin (BC) |
Instanton Floer homology from Heegaard diagrams |
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October 4 |
2pm | No seminar |
|
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October 11 |
2pm | No seminar |
|
|
October 18 |
2pm | Rohil Prasad (UC Berkeley) |
Low-action holomorphic curves and invariant sets |
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October 25 (Algebraic Topology seminar of interest!) |
11am in Room 507 | Rachael Boyd (Glasgow) |
Diffeomorphisms of reducible 3-manifolds |
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October 25 (double header!) |
2pm in Room 407 | Mark Powell (Glasgow) |
Corks for diffeomorphisms |
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October 25 (double header!) |
4pm in Room 520 | Chris Leininger (Rice) | Atoroidal surface bundles |
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November 1 |
2pm |
No seminar |
|
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November 8 (double header!) |
2pm |
Anubhav Mukherjee (Princeton) |
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November 8 (double header!) |
2pm |
Peter Feller (ETH Zurich) |
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November 15 |
2pm |
Xinle Dai (Harvard) | |
| November 22 |
2pm |
Casandra Monroe (UT Austin) | |
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November 29 |
2pm |
no seminar! |
Thanksgiving break |
|
December 6 (double header!) |
2pm | Giulio Tiozzo (UToronto) |
|
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December 6 (double header!) |
2pm | Matt Hedden (Michigan State) |
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Name: Ben Lowe
Title: Rigidity and Finiteness of Totally Geodesic Hypersurfaces in Negative Curvature
Abstract: There is a broad body of work devoted to proving theorems of the following form: spaces with infinitely many special sub-spaces are either nonexistent or rare. Such finiteness statements are important in algebraic geometry, number theory, and the theory of moduli space and locally symmetric spaces. I will talk about joint work with Simion Filip and David Fisher proving a finiteness statement of this kind in a differential geometry setting. Our main theorem is that a closed negatively curved analytic Riemannian manifold with infinitely many totally geodesic hypersurfaces must be isometric to an arithmetic hyperbolic manifold.
Name: Qiuyu Ren
Title: Lasagna s-invariant detects exotic 4-manifolds
Abstract: We introduce a lasagna version of Rasmussen's s-invariant coming from the study of Khovanov/Lee skein lasagna modules, which assigns either an integer or -\infty to each second homology class of a given smooth 4-manifold. After presenting some properties of the lasagna s-invariant, we show that it detects the exotic pair of knot traces X_{-1}(-5_2) and X_{-1}(P(3,-3,-8)). This gives the first gauge/Floer-theory-free proof of the existence of exotic compact orientable 4-manifolds. Time permitting, we mention some other applications of lasagna s-invariants. This is joint work with Michael Willis.
Name: John Baldwin
Title: Instanton Floer homology from Heegaard diagrams
Abstract: Heegaard Floer homology and monopole Floer homology are known to be isomorphic thanks to the monumental work of Taubes et al. But is there a simpler, more axiomatic explanation? And how is instanton Floer homology related to these other theories? I'll talk about work in progress with Zhenkun Li, Steven Sivek, and Fan Ye motivated by these questions. In particular, I'll sketch the construction of a chain complex that computes sutured instanton homology, which is isomorphic as a vector space to the Heegaard Floer chain complex of the sutured manifold. We are currently trying to prove that the differentials on the two sides agree.
Name: Rohil Prasad
Title: Low-action holomorphic curves and invariant sets
Abstract: Holomorphic curves are a very useful tool for studying the topology and dynamics of symplectic manifolds. I will start with an overview of how holomorphic curves can detect periodic orbits of symplectic diffeomorphisms, taking the viewpoint pioneered by Hofer in 1993. Then, I will discuss a new method using “low-action” holomorphic curves to detect closed invariant subsets that might be more general than periodic orbits. This has a few applications. I will mention one of them: a generalization to higher genus surfaces of a theorem by Le Calvez and Yoccoz. The talk is based on joint work with Dan Cristofaro-Gardiner, and will not assume any prior knowledge of holomorphic curves.
Name: Mark Powell
Title: Corks for diffeomorphisms
Abstract: I will present a cork theorem for diffeomorphisms of simply connected 4-manifolds, showing that one can sometimes localise a diffeomorphism to a contractible submanifold. I will sketch the proof and describe some applications. This is joint work with Slava Krushkal, Anubhav Mukherjee, and Terrin Warren.
Name: Chris Leininger
Title: Atoroidal surface bundles
Abstract: I will discuss joint work with Autumn Kent in which we construct the first known examples of compact atoroidal surface bundles over surfaces for which the base and fiber genus are both at least 2. This is a consequence of our construction of a type-preserving embedding of the fundamental group of the figure eight knot complement into the mapping class group of a thrice-punctured torus.