Date/Time : 03 Oct 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Dihua Jiang, University of Minnesota

I will discuss relations between non-abelian Fourier transforms and the Langlands conjecture on automorphic L-functions and associated local factors in the framework of Braverman-Kazhdan-Ngo.

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Date/Time : 03 Oct 2024 17:00
Venue : S17 #05-12 (SR4)
Speaker : Meng Fai Lim, Central China Normal University

In this talk, we begin reviewing the non-commutative Iwasawa theory as developed by Coates, Fukaya, Kato, Sujatha and Venjakob which is concerned with attaching suitable characteristic elements to modules of arithmetic interest (for instance, Selmer groups). By their construction, these characteristic elements are realized as element in an appropriate localized K_1 group. We then introduce a notion of “taking modulo p” of these characteristic elements and discuss some of its properties. This is an ongoing work with Chao Qin.

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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.

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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.

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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).

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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 : 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.

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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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