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Next seminar
Date: May 18 (Monday), 15:00-17:00
Place: 3-127
Speaker: Kyler Siegel
Title: Unicuspidal curves and cluster exchange graphs
Abstract: For some quantitative embedding problems in symplectic geometry, one can reduce the main difficulty to classifying certain singular algebraic curves. In the case of the complex projective plane these curves are now fairly well-understood, but even for other simple del Pezzo surfaces there is a whole complicated zoo of such curves. In this talk, I will explain how the formalism of cluster algebras gives a beautiful way of systematically organizing and understanding unicuspidal curves. In particular, they are organized into the exchange graph of an associated cluster algebra, and in some cases these exchange graphs have been fully worked out. This is the first step in a program to classify the so-called sesquicuspidal curves, which conjecturally give complete obstructions to stabilized ellipsoid embeddings. This is based on joint work in progress with D. McDuff.
Date: June 11 or 12 (TBD)
Place: TBA
Speaker: YuTung Yau
Title: Brane quantization and SYZ mirror symmetry
Abstract: Coisotropic A-branes were introduced by Kapustin and Orlov as an enlargement of the Fukaya category compatible with predictions from homological mirror symmetry. Despite substantial interest, however, a well-established mathematical framework for categories of such branes remains elusive.
In this talk, I will work in the semi-flat SYZ mirror symmetry setting and present a mathematical construction of the self-Hom spaces of semi-affine, space-filling coisotropic A-branes, based on joint work with K. Chan, N. C. Leung, Q. Li, and Y.-H. Suen. Our construction produces a non-formal holomorphic deformation quantization of the underlying A-model manifold.
This framework reflects ideas from the Gukov–Witten brane quantization proposal and family Floer theory, while also yielding a mirror correspondence identifying these A-model morphism spaces with the corresponding B-model morphism spaces on the mirror manifold. Furthermore, the induced actions on Lagrangian A-branes supported on torus fibers, together with their mirror B-branes, are shown to be functorial.
Past seminars
Date: January 21 (Wednesday), 13:00-15:00
Place: 3-108
Speaker: Laurent Côté
Title: Fukaya categories of conical symplectic resolutions
Abstract: Conical symplectic resolutions are a rather loosely defined class of hyperkähler varieties arising from canonical constructions in representation theory. Important examples include hypertoric varieties, Nakajima quiver varieties and Hitchin spaces. I will talk about Fukaya categories of conical symplectic resolutions. These are very rich objects, and they also turn out to be related to geometric representation theory. I will try to give an overview of this circle of ideas (much of which is not new in the symplectic literature). Any new content discussed in this talk is joint work with (subsets of) Benjamin Gammage, Justin Hilburn, Christopher Kuo, David Nadler and Vivek Shende.
Year:2026
Date: December 10 (Wed), 13:00-15:00
Place: 3-108
Speaker: Shanon J. Rubin
Title: A homotopical invariant of Weinstein surfaces
Abstract: In symplectic geometry, a Weinstein surface W can be understood by combinatorial data on its skeleton, which is generically a finite trivalent graph G. Motivated by the microlocal theory of sheaves, there is a naturally associated diagram D of differential-graded categories, defined over the quiver which replaces each edge of G by a cospan. We call such quivers ’graphic’. After adding in appropriate homological shifts, the homotopy limit of D yields an invariant of W, so we are motivated to find explicit presentations for these homotopy limits.
Abstracting the story above, we fix an arbitrary graphic quiver Q. Given any model category M (above we had M = dg-categories), we consider M-valued diagrams over Q. I will present a combinatorial characterization of all such diagrams D which are suitably Reedy-fibrant, which in particular implies that the homotopy limit of D is just its classical limit. This yields an explicit formula for the homotopy limit of any diagram, fibrant or not.
Date: November 13 (Thursday), 13:00-14:30 Irregular schedule!!
Place: 3-108
Speaker: Hiro Lee Tanaka
Title: Stable homotopy invariants in Floer theory (2nd talk)
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.
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: 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.
Year:2025
Organizers: Dogancan Karabas (TUJ), Tatsuki Kuwagaki