Date/Time : 29 Aug 2024 17:10
Venue : S17 #05-12 (SR4)
Speaker : Ma Jia Jun, Xiamen University and Xiamen University Malaysia

The speaker will share his personal experiences with Lean through this presentation. As undergraduate final year projects at Xiamen University Malaysia Campus, we have successfully formalized key concepts in game theory, including the Second-Price Auction and von Neumann’s Minimax Theorem. In collaboration with students from Xiamen University and the National University of Singapore, we have also made significant progress in formalizing results related to Lie algebras, Coxeter groups, and Kazhdan-Lusztig polynomials. The speaker will reflect on how formalization can deepen our understanding of mathematical concepts and its potential in teaching and research.

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Date/Time : 22 Aug 2024 17:00
Venue : S17 #05-12 (SR4)
Speaker : Chung Pang Mok, Soochow University

We justify (at least in a special case) the pseudorandomness of the vectors as constructed in the previous talk, by giving explicit discrepancy estimates. The main inputs are Erdos-Turan-Koksma type inequality for discrepancy estimation, and Bombieri-Weil bounds on certain kinds of exponential sums on elliptic curves over finite fields.

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Date/Time : 22 Aug 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Taiwang Deng, Beijing Institute of Mathematical Sciences and Applications

In this talk, I will explain the construction of a functor from the category of perverse sheaves on quiver varieties of type A to the category of perverse sheaves on flag varieties.We expect this functor to be dual to a functor introduced by K.Y. Chan and K. D. Wang recently which goes from the category of Harish-Chandra modules of GL(n,C) to the category of finite-dimensional modules of a graded Hecke algebra of type A. Moreover, dual (partial) Bernstein-Zelevinsky derivatives can be realized on quiver varieties via Lusztig induction and the latter can be shown to relate to the (dual) translation functor through our functor. This talk is based on my previous work as well as ongoing work with Chang Huang, Qixian Zhao, and Bin Xu.

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Date/Time : 21 Aug 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Chung Pang Mok, Soochow University

Using the arithmetic of elliptic curves over finite fields, we present an algorithm for the efficient generation of uniform pseudorandom vectors in high dimensions. We will also describe some numerical applications of the pseudorandom vector construction, including numerical integration in high dimensions and the numerical evaluation of Feynman-Kac formulas.

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Date/Time : 15 Aug 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Felix Schremmer, The University of Hong Kong

If a Shimura variety is fully Hodge-Newton decomposable, its mod p reduction enjoys particularly nice properties. These cases are well-understood and characterized by a certain inequality known as the minute condition. In a joint project in progress with Xuhua He and Eva Viehmann, we study the next larger cases, where the minute condition is barely not satisfied any more. I will give a classification of these cases and explain the geometric properties of the corresponding Ekedahl-Oort and Kottwitz-Rapoport strata. If time permits, I will also talk about the local model in the case of Iwahori level structure, and where to find it in the affine flag variety.

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Date/Time : 15 Aug 2024 17:00
Venue : S17 #05-12 (SR4)
Speaker : Qingchao Yu, The University of Hong Kang

Steinberg’s cross-section is a transversal slice of the regular unipotent orbit of connected reductive group. It has been generalized to unipotent orbits by the work of He-Lusztig and Duan, using Lusztig’s map and the notion of good position elements. In this talk, we first recall the theory of Steinberg’s cross-section and then
generalize it using the notion of convex elements of the Weyl group. We show that the U-conjugation property, which plays an essential role in the construction of He-Lusztig, holds for convex elements. Moreover, all good position elements are convex.

This is based on my recent joint work with Sian Nie and Panjun Tan.

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Date/Time : 24 Jul 2024 16:00
Venue : S17 #04-05 (SR2)
Speaker : Jonas Antor, University of Oxford

Affine Hecke algebras are deformations of group algebras of affine Weyl groups that play an important role in the representation theory of p-adic groups. In their groundbreaking work, Kazhdan and Lusztig found a geometric realization of the affine Hecke algebra via equivariant K-theory. This allowed them to prove the Deligne-Langlands correspondence, a special case of the local Langlands conjecture that gives a geometric parametrization of the irreducible representations of this algebra. In this talk, we will discuss a categorical version of this Deligne-Langlands correspondence that relates (dg-)modules over the affine Hecke algebra with certain categories of constructible sheaves. Time permitting, we will also talk about some work in progress that
attempts to construct new geometric realizations of affine Hecke algebras with unequal parameters which control a larger part of the representation theory of p-adic groups.

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Date/Time : 20 Jun 2024 14:00
Venue : S17 #04-05 (SR2)
Speaker : Sunil Chebolu, Illinois State University

More than 50 years ago, Fuchs asked which abelian groups can be the group of units of a commutative ring? Though progress has been made, the question remains open. I will present an overview of my joint work with Keir Lockridge on this problem. We answered this question for various classes of groups including indecomposable abelian groups, dihedral groups, quaternion groups and some p-groups. This work also gave us several new characterizations of Mersenne primes and Fermat primes.

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Date/Time : 10 May 2024 15:00
Venue : S17 #04-06 (SR1)
Speaker : Erez Lapid, Weissman Institute of Science

Prehomogeneous vector spaces are ubiquitous in the theory of nilpotent orbits of semisimple Lie algebras. Their study was initiated by M. Sato in the 1960s. Zeta functions attached to them are useful for the asymptotics of arithmetic invariants. They are also important in the geometric side of Arthur’s trace formula. I will discuss some recent work on the analysis of these zeta functions.

Joint work with Tobias Finis.

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