Fall 2020

Place: Zoom Meeting Room (Virtual)
Time: Thursdays 3:00pm-4:00pm (CT)
Zoom Meeting ID: 988 8144 3994 (Email Dogancan Karabas to access the meeting password.)
The meeting room opens at 2:45pm and closes at 4:30pm.
Organizers: Ezra Getzler, Dogancan Karabas (dogancan.karabas[at]northwestern dot edu), and Eric Zaslow

October 8, 2020

  • Speaker: Sangjin Lee (IBS Center for Geometry and Physics)
  • Title: Higher dimensional generalization of pseudo-Anosov automorphisms
  • Abstract: In the 70’s, Thurston classified the mapping class groups of surfaces. The main idea is to observe what happens under the iteration of a mapping class. In this talk, we will apply the idea on a symplectic manifold. More precisely, we will see what happens when a symplectic automorphism is iterated and we will discuss a Lagrangian lamination which is obtained by the iteration.
  • Notes: Slides
  • Recording: Zoom

October 15, 2020

  • Speaker: Dimitri Zvonkine (IMJ-PRG)
  • Title: Quantum Hall effect and vector bundles over moduli spaces of curves and Jacobians
  • Abstract: Vector bundles of so-called Laughlin states were introduced by physicists to study the fractional quantum Hall effect. Their fibers are spaces of ground states of a gas of particles on a surface and their Chern classes are measurable physical quantities. We will explain how they are related to the vector bundle of theta-functions over the moduli space and to certain vector bundles over the Jacobians. We report some computations of their ranks and Chern classes. Work in progress with Semyon Klevtsov.
  • Recording: Zoom

October 22, 2020

  • Speaker: Roger Casals (UC Davis)
  • Title: Legendrian knots and Lagrangian fillings
  • Abstract: This will be an introductory talk to Legendrian knots and the modern techniques for their study. In the course of 2020 we are gaining significant understanding in the study of Legendrian links in the 3-sphere. Part of these developments focus on the study of their Lagrangian fillings: particular surfaces in 4-dimensional symplectic space which bound these knots. In this talk, I will survey the main advances that are taking place by presenting examples, geometric arguments and pictures. In particular, I will discuss the currently available methods to show that a given Legendrian link admits infinitely many Lagrangian fillings, sprouting from the initial January 2020 discovery (with H. Gao), which will also be discussed.
  • Notes: Slides
  • Recording: Zoom

October 29, 2020

  • Speaker: Jeff Hicks (University of Cambridge)
  • Title: Lagrangian surgery, antisurgery, and dimers
  • Abstract: In this talk I will show how to use Lagrangian surgery to construct a tropical Lagrangian submanifold in (C^*)^n from the data of a dimer on a torus. We will use Haug’s antisurgery technique to build “mutations” of this Lagrangian, and see how this operation is reflected in certain manipulations of the dimer. Finally, we will discuss how the Floer theoretic support of this Lagrangian is related to Treumann, Williams and Zaslow’s work on the Kasteleyn operator and mirror symmetry.
  • Notes: PDF
  • Recording: Zoom

November 5, 2020

  • Speaker: Ben Webster (University of Waterloo and Perimeter Institute for Theoretical Physics)
  • Title: Hypertoric mirror symmetry
  • Abstract: I’ve frequently heard the assertion that “hyperkahler manifolds are self-mirror up to rotation.” I’m not so sure this is true in general, but I know one example of such a variety:  multiplicative hypertoric varieties; these are what happens when you cut up a real torus into polytopes, and then send the polytopes to have a toric hyperkahler party.  I’ll discuss recent work with Gammage and McBreen showing that self-homological homological mirror symmetry after rotation holds in this case and do my best to show how this fits in with a larger story of K-theoretic Coulomb branches.
  • Notes: Slides
  • Recording: Zoom

November 12, 2020

  • Speaker: Pierrick Bousseau (Paris-Saclay)
  • Title: The skein algebra of the 4-punctured sphere from curve counting
  • Abstract: The Kauffman bracket skein algebra is a quantization of the algebra of regular functions on the SL_2 character variety of a topological surface. I will explain how to realize the skein algebra of the 4-punctured sphere as the output of a mirror symmetry construction based on higher genus Gromov-Witten invariants of a log Calabi-Yau cubic surface. This leads to a proof of a previously conjectured positivity property of the bracelets bases of the skein algebras of the 4-punctured sphere and of the 1-punctured torus.
  • Notes: Slides
  • Recording: Zoom

November 19, 2020

  • Speaker: Sheel Ganatra (University of Southern California)
  • Title: A user’s guide to (partially) wrapped Fukaya categories
  • Abstract: I will describe a package of structural results for (partially) wrapped Fukaya categories — sufficient in many cases to give black-box computations — and some relationships to noncommutative geometry, mirror symmetry, and sheaf theory.  This is joint work with J. Pardon and V. Shende.
  • Notes: PDF
  • Recording: Zoom

December 3, 2020

  • Speaker: Hülya Argüz (Versailles, Paris-Saclay)
  • Title: Enumerating log maps via wall-crossing
  • Abstract: Punctured log Gromov—Witten invariants of Abramovich—Chen–Gross—Siebert are obtained by counting of stable maps with prescribed tangency conditions (which are allowed to be negative) relative to a not necessarily smooth divisor. In this talk we describe an algorithmic method to compute punctured log Gromov-Witten invariants of log Calabi-Yau varieties, which are obtained by blowing-up of toric varieties along hypersurfaces on the toric boundary. For this we use tropical geometry and wall-crossing computations. This is joint work with Mark Gross (arxiv:2007.08347).
  • Notes: Slides
  • Recording: Zoom

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