关于举行代数拓扑与几何系列学术研讨会III的通知

报告人

报告题目及摘要

时间

Yun Shi (Brandeis University)

报告题目: D-critical locus structure for local toric Calabi-Yau 3-folds

报告摘要: Donaldson-Thomas (DT) theory is an enumerative theory which produces a virtual count of stable coherent sheaves on a Calabi-Yau 3-fold. Motivic Donaldson-Thomas theory, originally introduced by Kontsevich-Soibelman, is a categorification of the DT theory. This categorification contains more refined information of the moduli space. In this talk, I will explain the role of d-critical locus structure in the definition of motivic DT invariant, following the definition by Bussi-JoyceMeinhardt. I will also discuss results on this structure on the Hilbert schemes of zero dimensional subschemes on local toric Calabi-Yau threefolds. This is based on joint works with Sheldon Katz. The results have substantial overlap with recent work by Ricolfi-Savvas, but techniques used here are different.

8:00-9:00

Lutian Zhao (University of Maryland)

报告题目: Stability of Parahoric Higg Bundle

报告摘要: Parahoric Higgs bundle is a type of Higgs bundle that allows an introduction of wild singularity. Pararhoric G-Higgs bundle is similar to parabolic Higgs bundle where we replace the parabolic subgroup in the definition with a parahoric subgroup in the context of Bruhat-Tits. In this talk, I will describe the stability conditions motivated by the work of ramanathan, that prove to be important in establishing the non-Abelian Hodge correspondence in this setup. This is joint work with Pengfei Huang, Georgios Kydonakis, and Hao Sun.

9:10-10:10

Wenwei Li (Peking University)

报告题目: Higher localization and applications to higher branching laws

报告摘要: Given a complex variety X on which a connected reductive group G acts, the localization functor is a simple recipe that produces DX-modules from g-modules. This includes the well-known Beilinson-Bernstein localization for flag varieties as a particular case. In the first part of the work, I will present an equivariant and derived version of localization, which is best phrased in terms of h-complexes and h-derived categories of Beilinson-Ginzburg. It turns out that when X is an affine spherical homogeneous space and K is a reductive spherical subgroup of G, the localizations of Harish-Chandra (g, K)-modules have regular holonomic cohomologies. In the second part of the talk, I will explain how higher localization can be applied to the study of higher branching laws, as proposed by Dipendra Prasad, in the algebraic context of (g, K)-modules. If time permits, I will also try to relate the algebraic and analytic pictures.

10:30-11:30

Yu Zhao (University of Tokyo)

报告题目: A Weak Categorification of the quantum toroidal algebra actions

报告摘要: We will explain a new construction of a weak categorification of the quantum toroidal algebra action on the Grothendieck group of moduli space of stable (or framed) sheaves over an algebraic surface. At the level of K theory, this action is constructed by Schiffmann-Vasserot and Negut¸

14:00-15:00

Chenglong Yu (Tsinghua University)

报告题目: Commensurabilities among Lattices in P U(1, n)

报告摘要: The study of hypergeometric functions dates back to Euler and Riemann. The global monodromy groups arising from analytic continuations of those functions play an important rule in their global properties. Many mathematicians including Fuchs, Schwarz, Picard, Pochhammer, Appell, Lauricella and Terada studied the corresponding period integrals and higher dimensional generalizations. In 1980’s, Deligne and Mostow obtained complete discreteness and arithmeticity criteria for those monodromy groups acting on complex hyperbolic balls. Thurston also gave another approach via flat conic metrics. On the other hand, the classification of those groups up to conjugation and finite index (commensurability) is not completed. The dimension one case is the classical hyperbolic triangle groups and solved by work of Greenberg, Petersson, Singerman and Takeuchi. There are some commensurability results on dimension two case by Sauter and Deligne-Mostow. In this talk, we will discuss some new results on commensurabilities among lattices in P U(1, n) for higher dimension n. The results rely on constructions of higher dimensional varieties instead of analysis of complex reflection groups. This approach also gives new proofs for existing results in n=2. This is joint work with Zhiwei Zheng.

15:30-16:30