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Next seminar
Date: October 22 (Wed), 13:00-15:00
Place: 3-127
Speaker: Tomohiro Asano
Title: TBA
Abstract: TBA (He will speak about his new paper)
Date: November 5 (Wed), 10:00-12:00 Irregular schedule!!
Place: 3-110
Speaker: Hiro Lee Tanaka
Title: Stable homotopy invariants in Floer theory
Abstract: After introducing the basics of stable homotopy theory (also known as the theory of spectra, or as algebra over the sphere), we will motivate the pursuit of stable-homotopy-theoretic invariants in geometry (with a focus on Floer theory and symplectic geometry). If time allows, we will also discuss three different existing approaches to produce Fukaya categories whose coefficients are not integral, but are linear over the sphere.
Past seminars
Date: September 17 (Wed), 13:00-15:00
Place: 3-127
Speaker: Kazuki Kudomi (Tohoku University)
Title: On characteristic cycles of some irregular holonomic D-modules
Abstract: For a holonomic D-module M on a complex manifold X, we define the conic Lagrangian cycle CC(M) on the cotangent bundle T*X. This cycle is called the characteristic cycle of M.
Building on the theory of meromorphic connections developed by Sabbah, Mochizuki and Kedlaya, D’Agnolo–Kashiwara established the Riemann–Hilbert correspondence for (not necessarily regular) holonomic D-modules. In this talk, as an application of this correspondence, we calculate the characteristic cycles for some irregular holonomic D-modules and give a generalization of Ginzburg’s formula for the limit of characteristic cycles.
This talk is based on joint work with Kiyoshi Takeuchi.
Date: August 7 (Thu), 13:00-15:00 Irregular schedule!!
Place: 3-552
Speaker: Tianyu Yuan (Eastern Institute of Technology, Ningbo)
Title: Orbifold Lagrangian Floer theory and Hecke algebras
Abstract: Let G be a finite group acting on X. We show that the wrapped Fukaya algebra of a generic fiber of T^*(X/G) is isomorphic to the Hecke algebra associated to X/G. The key ingredient in defining such orbifold Floer theory is the global Kuranishi chart developed by Abouzaid-Mclean-Smith and Bai-Xu. This is joint work in progress with Ko Honda, Roman Krutowski, and Yin Tian.
Date: July 10 (Thu), 13:00-15:00 Irregular schedule!!
Place: 3-127
Speaker: Wenyuan Li (University of Southern California)
Title: Lagrangian correspondence in topological Fukaya categories
Abstract: Lagrangian correspondences between symplectic manifolds are generalizations of symplectomorphisms and are expected to give the morphisms in the 2-category of symplectic manifolds under geometric compositions. For the (wrapped) Fukaya categories of certain exact symplectic manifolds, by the Kunneth formula, exact Lagrangian correspondences define bimodules over the categories. We will consider the topological model of (wrapped) Fukaya categories of Weinstein manifolds in terms of microlocal sheaves and show that the geometric composition of Lagrangian correspondences agrees with the algebraic composition of bimodules. This is joint work in preparation with David Nadler and Vivek Shende.
Date: June 26 (Thu), 13:00-15:00 Irregular schedule!!
Place: 3-552
Speaker: Hayato Morimura (Kavli IPMU)
Title: Remarks on the Fukaya categories of singular hypersurfaces
Abstract: This talk is based on my survey on the Fukaya categories on singular hypersurfaces. Auroux proposed a definition of the Fukaya category of a singular hypersurface as the localization of that of a nearby fiber at the clockwise monodromy autoequivalence. Jeffs showed that it is equivalent to the Fukaya-Seidel category of the associated Liouville Landau-Ginzburg model (Knorrer periodicity). In this talk, I will outline his proof and present some of my observations. On the way, I will explain background materials, ignoring additional data on Lagrangians such as grading and orientation.
Date: June 4 (Wed), 13:00-15:00
Place: 3-108
Speaker: Dogancan Karabas (Kyoto University)
Title: From Weinstein Manifolds to Finite Quivers
Abstract: Kontsevich conjectured that the wrapped Fukaya category of any finite-type (Wein)stein manifold is Morita equivalent to a dg algebra of finite type, that is, the path algebra of a finite graded quiver with differential. I will outline a proof in three steps: (1) a local-to-global gluing description of Fukaya categories via Ganatra–Pardon–Shende, (2) a local model for Weinstein manifolds using arboreal singularities, whose Fukaya categories are finite-type by work of Nadler, and (3) a cofibration category structure on the category of dg categories, developed with Sangjin Lee and myself, which ensures that gluing preserves finite-typeness. I will also explain the necessary background and definitions along the way.
Organizers: Dogancan Karabas, Tatsuki Kuwagaki