日程 Schedule

8月26日 (Aug. 26)

8:30-9:30 付保华Baohua Fu（AMSS）

茶歇Tea break

10:00-11:00肖梁Liang Xiao（BICMR）

11:10-12:10 苏长剑Changjian Su（YMSC）

午餐Lunch

14:00-15:00 贾博名Boming Jia (YMSC)

茶歇Tea break

15:30-16:30 Marc Besson (BICMR)

8月27日 (Aug. 27)

8:30–9:30 Dylan Allegretti (YMSC)

茶歇Tea break

10:00-11:00 李鹏程Pengcheng Li (YMSC)

11:10-12:10 胡越Yue Hu (YMSC)

Upcoming talks:

题目：A new infinite family of isolated symplectic singularities

报告人：付保华 Baohua Fu（AMSS）

时间：2022/08/26 8:30-9:30am

会议：https://us06web.zoom.us/j/2763667254?pwd=b0JoMWNBVFN4c0JXcmI0L01tblIxQT09

摘要： We construct a new infinite family of 4-dimensional isolated symplectic singularities with trivial local fundamental group, answering a question of Beauville raised in 2000. Three constructions are presented for this family: (1) as singularities in blowups of the quotient of C4by the dihedral group of order 2d, (2) as singular points of Calogero-Moser spaces associated with dihedral groups of order 2dat equal parameters, (3) as singularities of a certain Slodowy slice in the d-fold cover of the nilpotent cone in sl_d.  

This is a joint work with G. Bellamy, C. Bonnafé, D. Juteau, P.  Levy, E. Sommers.

题目：Arithmetic applications of geometric aspects of Shimura varieties

报告人：肖梁Liang Xiao（BICMR）

时间：2022/08/26 10:00-11:00am

会议：https://us06web.zoom.us/j/2763667254?pwd=b0JoMWNBVFN4c0JXcmI0L01tblIxQT09

摘要： Geometric properties of Shimura varieties can provide us with access to arithmetic information in Langlands program. I will survey several typical topics and scenarios where we encounter such applications. Hopefully, we can convey the geometric representation-theoretic input to such results.

题目：Positivity of the CSM classes and cohomology of Hessenberg varieties

报告人：苏长剑Changjian Su（YMSC）

时间：2022/08/26 11:10am-12:10pm

会议：https://us06web.zoom.us/j/2763667254?pwd=b0JoMWNBVFN4c0JXcmI0L01tblIxQT09

摘要：The talk aims to introduce two problems I am thinking about. I will first talk about Kumar's conjecture about the positivity of the Chern-Schwartz-MacPherson (CSM) classes of the Richardson cells. Then the talk will be devoted to the Stanley-Stembridge conjecture about the chromatic symmetric function, which can be reformulated using the symmetric group action on the cohomology of the regular semisimple Hessenberg varieties. Using the Fourier transform, we can reprove the conjecture for the parabolic case. We also hope the CSM class theory can shed some light on this conjecture.

题目：The Geometry of the Affine Closure of T^*(G/U).

报告人：贾博名Boming Jia (YMSC)

时间：2022/08/26 2:00-3:00pm

会议：https://us06web.zoom.us/j/2763667254?pwd=b0JoMWNBVFN4c0JXcmI0L01tblIxQT09

摘要： The affine closure of T^*(G/U) has been expected to have symplectic singularities in the sense of Beauville. We prove this conjecture for the special case G=SL_n. When n=3, this affine closure is isomorphic to the closure of the minimal nilpotent orbit O_min in so(8,C). Moreover, in this case, the quasi-classical Gelfand-Graev action of the Weyl group W=S3 on (T^*(SL3/U))^aff can be identified as the restriction of Cartan’s triality S3-action on so(8) to the closure of the minimal orbit O_min. We will also discuss about Kostant’s theorem on highest weight varieties, and we will see that in the case of minimal nilpotent orbit closure in so(2m), there is an interpretation (and proof) of this theorem via Hamiltonian reduction.

题目：Demazure polytopes and GIT

报告人：Marc Besson(BICMR)

时间：2022/08/26 3:30-4:30pm

会议：https://us06web.zoom.us/j/2763667254?pwd=b0JoMWNBVFN4c0JXcmI0L01tblIxQT09

摘要：This introductory talk will begin with an overview of Schubert varieties and Demazure modules in a variety of settings. Demazure modules play the role of providing filtrations for many spaces which arise naturally in representation theory, such as weight multiplicity spaces and tensor decomposition multiplicity spaces, in both the affine and finite settings. In the second part of the talk, I will discuss some applications of Geometric Invariant Theory (GIT) to the combinatorics of Demazure modules (recent work by B., Jeralds, Kiers). Moreover I will discuss an ongoing project which generalizes these results to the affine setting.

题目：From triangulated categories to Teichmüller spaces

报告人：Dylan Allegretti(YMSC)

时间：2022/08/27 8:30–9:30am

会议：https://us06web.zoom.us/j/2763667254?pwd=b0JoMWNBVFN4c0JXcmI0L01tblIxQT09

摘要：I will start by reviewing a construction of V. Ginzburg, which associates a 3-Calabi-Yau triangulated category to a quiver with potential. I will then describe a relationship between the space of Bridgeland stability conditions on such a category and the Teichmüller space of a surface.

题目：Categorical actions and derived equivalences for finite odd-dimensional orthogonal groups

报告人：李鹏程Pengcheng Li (YMSC)

时间：2022/08/27 10:00-11:00am

会议：https://us06web.zoom.us/j/2763667254?pwd=b0JoMWNBVFN4c0JXcmI0L01tblIxQT09

摘要：In this talk, I will give a brief introduction to Kac-Moody categorification and Broue's abelian defect group conjecture. We prove that Broue's abelian defect group conjecture is true for the finite odd-dimensional orthogonal groups SO_{2n+1}(q) at linear primes with q odd. We frist make use of the reduction theorem of Bonnafe-Dat-Rouquier to reduce the problem to isolated blocks. Then we construct a categorical action of a Kac-Moody algebra on the category of quadratic unipotent representations of the various groups SO_{2n+1}(q) in non-defining characteristic, by generalizing the corresponding work of Dudas-Varagnolo-Vasserot for unipotent representations. This is one of the main ingredients of our work which may be of independent interest. To obtain derived equivalences of blocks and their Brauer correspondents, we define and investigate isolated RoCK blocks. Finally, we establish the desired derived equivalence based on the work of Chuang-Rouquier that categorical actions provide derived equivalences between certain weight spaces. This is a joint work with Yanjun Liu and Jiping Zhang.

题目：Specialization maps for shuffle algebras of type $B_{n}$ and $G_{2}$.

报告人：胡越 Yue Hu (YMSC)

时间：2022/08/27  11:10am-12:10pm

会议：https://us06web.zoom.us/j/2763667254?pwd=b0JoMWNBVFN4c0JXcmI0L01tblIxQT09

摘要：We define a filtration of Feigin-Odesskii's shuffle algebras in type $B_{n}$ and $G_{2}$ using specialization maps, generalizing the results in type $A_{n}$ given by Negut and Tsymbaliuk. As an application, we construct a class of PBW basis for the positive part of quantum affine algebras in New Drinfeld realizations.