几何表示论讨论班

组织者 Organizer:Will Donovan,单芃, 李鹏辉
时间 Time: 周五, 3:20-4:20 pm,2021-3-5 ~ 6-25
地点 Venue:宁斋 W11

报告摘要 Abstract



Upcoming talks


Date: June 4, 2021, 3:20 to 4:20 PM

Zoom Meeting ID:3610386975
Password:BIMSA
Speaker: Quoc Ho (IST Austria)
Title: Factorization homology and the arithmetic and topology of configuration spaces
Abstract: The last decade has witnessed many interesting interplays between homological/representation stability phenomena and questions in arithmetic statistics. In this talk, I will show how the algebro-geometric version of factorization homology provides a unifying framework for studying these phenomena in the case of configuration spaces. In particular, I will explain the relationship between various zeta values coming out of point-counts on configuration spaces and homological stability phenomena exhibited by these spaces, answering questions of Farb--Wolfson--Wood. Time permitting, I will explain how these ideas can be further developed to study representation stability for ordered configuration spaces.



Past talks


Date: May 14, 2021, 3:20 PM to 4:20 PM
Speaker: Lin Xun
Title:Noncommutative Hodge conjecture
Abstract: I will propose a rational Hodge conjecture for small smooth proper dg categories. The Hodge conjecture of Per_{dg}(X) is equivalent to the rational Hodge conjecture of projective smooth variety X. The Hodge conjecture is additive to the semi-orthogonal decompositions. Using semi-orthogonal decompositions, especially from HPD,  we obtain some interesting examples. Motivated from these examples, we expect that the dual statement of Hodge conjecture for linear sections of projective dual varieties can be proved by geometric methods. In this talk, there will be more questions than theorems.



Date: May 7, 2021, 3:20 PM to 4:20 PM
Zoom Meeting ID:3610386975
Password:BIMSA
Speaker: Syu Kato (Kyoto University)
Title: Categorification of DAHA and Macdonald polynomials
Abstract: We exhibit a categorification of the double affine Hecke algebra (DAHA) associated with an untwisted affine root system (except for type $G$) and its polynomial representation by using the (derived) module category of some Lie superalgebras associated to the root system. This particularly yields a categorification of symmetric Macdonald polynomials. This is a joint work with Anton Khoroshkin and Ievgen Makedonskyi.


                                                                                                                                                                                                                                                            


Date: Apr 23, 2021, 3:20 PM to 4:20 PM

Place: Ning Zhai W11
Speaker:  李鹏辉 Penghui Li

Title:Eisenstein series via factorization homology of Hecke categories.

Abstract: Motivated by the spectral gluing patterns in the Betti Langlands program. We define the E_2 Hecke category as the category of coherent sheaves on moduli stacks of G-bundles on a disk with parabolic reduction on the boundary circle. We prove that its factorization homology is the (enhanced) Eisenstein series category. Our results naturally extend previous known computations of Ben-Zvi--Francis--Nadler and Beraldo. This is a joint work with Quoc Ho.




Date: Apr 16, 2021, 3:20 PM to 4:20 PM

Zoom Meeting ID:3610386975
Password:BIMSA
Speaker: Tatsuki Kuwagaki

Title:Sheaf quantization and irregular singularity
Abstract:Constructible sheaves have played an important role in the development of representation theory. The topic of this talk is sheaf quantization, which is a geometric refinement of the notion of constructible sheaf (“constructible sheaf (or local system) of 21st century”). I will give an introduction to sheaf quantization and discuss how it is difficult (at present) to construct it in general and its relation to irregular singularities. 




Date: Apr 1, 2021, 8:00 AM to 9:00 AM
Place: Ning Zhai W11

Zoom Meeting ID:3610386975
Password:BIMSA
Speaker: Nicolas Addington

Title:A categorical sl_2 action on some moduli spaces of sheaves
Abstract:We study certain sequences of moduli spaces of sheaves on K3 surfaces, building on work of Markman, Yoshioka, and Nakajima. We show that these sequences can be given the structure of a geometric categorical sl_2 action in the sense of Cautis, Kamnitzer, and Licata. As a corollary, we get an equivalence between derived categories of some moduli spaces that are birational via stratified Mukai flops. I'll spend most of my time on a nice example. This is joint with my student Ryan Takahashi.






Date: Mar. 24th, Wednesday, 8:00-9:00 am
Zoom Meeting ID:3610386975
Password:BIMSA
Speaker: David Nadler (UC Berkeley)
Title: Hecke bubbling in Betti Geometric Langlands
Abstract: I'll discuss joint work with Zhiwei Yun that reformulates Hecke actions in terms of bubbling projective lines at marked points of curves. Our motivation is to relate automorphic categories for smooth curves and their nodal degenerations.




Date: Mar. 12th, 2021
Place: Ning Zhai W11
Speaker: 陈伟彦 CHEN Weiyan 
Title: Topology and Arithmetic Statistics
Abstract: Topology studies the shape of spaces. Arithmetic statistics studies the behavior of random algebraic objects such as integers and polynomials. I will talk about a circle of ideas connecting these two seemingly unrelated areas. To illuminate the connection, I will focus on two concrete examples: (1) the Burau representation and superelliptic curves, and (2) cohomology of the space of multivariate irreducible polynomials.



Date: Mar. 5th
Speaker: Lin Chen 陈麟 (Harvard University)
Title: nearby cycles and long intertwining functor
Abstract: Let G be a reductive group and (N,N^-) be the unipotent radicals of a pair of opposite Borel subgroups (B,B^-). The well-known long intertwining functor is an equivalence from the category Shv(Fl)^N of N-equivariant sheaves on the flag variety Fl to the similar category Shv(Fl)^{N^-} for N^-. We will interpret this equivalence as a duality between the above two categories, and explain that the unit object for this duality can be obtained as nearby cycles along a Vinberg-degeneration of Fl. We also describe an affine analogue of this result and explain its relation with Bernstein’s second adjointness.




iCal subscription:
webcal://p44-caldav.icloud.com/published/2/MTAyNjc3ODU1NDUxMDI2N6u0UZbdquLXYBj0BHqibhq2tnAyUQL92ZssPrsxYupRMNYLbinA3gkvQW2gWiMfGim4dkQcHMpsiPnhEkftcUc