Date/Time : 23 Sep 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : David Schwein, University of Bonn

Supercuspidal representations are the elementary particles in the representation theory of reductive p-adic groups. Constructing such representations explicitly, via (compact) induction, is a longstanding open problem, solved when p is large. When p is small, the remaining supercuspidals are expected to have an arithmetic source: wildly ramified field extensions. In this talk I’ll discuss ongoing work joint with Jessica Fintzen that identifies a second, Lie-theoretic, source of new (tame!) supercuspidals: special features of root systems at very small primes.

Add to calendar :

Date/Time : 12 Sep 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Kyo Nishiyama, Aoyama Gakuin University

Let $ G = Sp_{2n}(\R) $ (or $ U(n, n) $) and $ P $ a maximal parabolic subgroup stabilizing a Lagrangian subspace (Siegel parabolic subgroup). Let $ H \simeq GL_n(\R) $ be a Levi subgroup of $ P $, which is also a symmetric subgroup of $ G $. We choose a parabolic subgroup $ Q \subset H $.

Let $ X = H/Q \times G/P $ be a real double flag variety on which $ H $ acts diagonally. We are interested in the geometry of $ X $. For example, there are only finitely many $ H $-orbits on $ X $, so that it is of finite type.

In this talk, we introduce integral kernel operators which intertwine degenerate principal series of $ G = Sp_{2n}(\R) $ and $ H = GL_n(\R) $. For the kernel of the operator, we use relative invariants associated with a prehomogeneous vector space naturally arising from the geometry of $ X $. The integrals have complex parameters, and at certain integral parameters we get finite dimensional representations as images.

Add to calendar :

Date/Time : 05 Sep 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Ning Li, Nankai University

The notion of transfer is a way to relate representation theory of different real forms of a complex semisimple Lie group. In this talk, I will explicitly describe the transfer of \theta(1) of Sp(2n,R) in the case of non-stable range via the study of K-types. As a corollary, we get certain compatibility of local theta correspondence and the transfer functor, and every unitary irreducible constituent of degenerate principal series of maximal Gelfand-Kirillov dimension is a derived functor module, which coincide with the results of Matumoto-Trapa for the case of Sp(p,q), SO*(2n), and U(m,n).

Add to calendar :

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.

Add to calendar :

Date/Time : 29 Aug 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Zeng Haozhi , Huazhong University of Science and Technology

The Peterson variety is introduced by Dale Peterson to describe the quantum cohomology rings of all the partial flag varieties. In this talk, we discuss an explicit morphism from the Peterson variety to the Blume toric orbifold. As an application, we calculate the totally nonnegative part of the Peterson variety in Lie type A and give a proof of Rietsch’s conjecture. This is joint work with Hiraku Abe.

Add to calendar :

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.

Add to calendar :

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.

Add to calendar :

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.

Add to calendar :

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.

Add to calendar :