Speaker: Daniel Wong (黄家裕) 香港中文大学深圳校区
Abstract: The Harish-Chandra Lefschetz principle says that there are similarities between the representation theories for real and $p$-adic groups. In this talk, we give one account of such resemblences by constructing an exact functor from the category of Harish-Chandra modules of $GL(n,\mathbb{C})$ to the category of finite-dimensional modules of graded Hecke algebra $\mathcal{H}_m$ of Type $A$. We will show that the functor preserves parabolically induced modules, standard modules, irreducible modules, unitary modules and Dirac series. It also links a Bernstein-Zelevinsky type functor in $\mathcal{H}_m$-module side to tensor decomposition problems on the $GL(n,\mathbb{C})$-module side. This is a joint work with Kei Yuen Chan.
Room: 216, East 32 Building.
Time: April 9, 10:30
Speaker: 薛江维 武汉大学
Abstract: The notion ``selectivity" is first introduced by Chinburg and Friedman in 1999 to describe the phenomenon that certain quadratic orders tend to embed into some but not all maximal orders in a fixed indefinite quaternion algebra, as if they have selected some maximal order to embed into. This theory was further developed by Chan and Xu, Guo and Qin, and many others. However, most of the development focus on the indefinite case (i.e., when the quaternion algebra satisfies the Eichler condition). In this talk, we explain the generalization of the selectivity theory to the totally definite case and then apply it to obtain several refined class/type number formulas for totally definite quaternion orders. Such formulas enable us to prove certain divisibility results about these class/type numbers. This talk is based on joint works with Yucui Lin and Chia-Fu Yu.
Room: 216, East 32 Building.
Time: April 23, 10:30
Speaker: Nadir Matringe 上海纽约大学
Abstract: I will present an ongoing work with Omer Offen and Chang Yang on local global principles for certain periods of automorphic representations of inner forms of GL(n). In particular it implies the direct implication of a conjecture of Guo and Jacquet, without any local restriction on the global representation.
Room: 216, East 32 Building.
Time: April 28, 15:30
Speaker: 洪钰郎 华中科技大学
Abstract: L-functions played an important role in the development of algebraic number theory.In this talk,I will give two examples .The first example is to prove the Chebetorarev density theorem using the anylatic properties of L-functions .Then I will show how Chebetararev density theorem helps us to prove the existance of primes satisfying certain conditions. The second application is to derive the class number formula for abelian number fields from the arithmetic properties of L -functions. I will also calculate in detail for some quadratic fields to show how powerful the formula is.
Room: 216, East 32 Building.
Time: May 13, 14:30-15:30
Speaker: 陈垣宇 华中科技大学
Abstract: The irreducible cuspidal representation of GL (2,F) is an important component in the representation theory of p-adic groups. In the first part we investigate strata on GL(2,F) to establish a relationship with some “special” cuspidal representations. It leads to our first main result——Exhaustion Theorem. Then we want to generalize our findings to all cuspidal representations. Through the cuspidal types on GL(2,F), we establish the Induction Theorem, our second main result. Finally, we construct cuspidal types from tamely ramified quadratic extensions E over the p-adic field F. From this, we get Tame Parametrization Theorem.
Room: 216, East 32 Building.
Time: May 16, 14:30-15:30
Speaker: Daniel Skodlerack 上海科技大学
Abstract: (Joint work with Robert Kurinczuk, Shaun Stevens, David Helm) In this talk we present how to get the block decompositions for the category of smooth representations of a p-adic classical group with coefficients in a very general integral domain in which p is invertible. It is done in two steps: First in decomposing via endo-parameters and then decomposing for an endo-parameter the subcategory into blocks along block-decompositions for finite groups passing through the vertexes of a chamber of a building associated to the end-parameter.
Room: 216, East 32 Building.
Time: May 21, 10:30-11:30
Speaker: 蒋泽旭 华中科技大学
Abstract: As important geometric objects, Grassmann spaces hold a significant position in numerous mathematical fields and inherently embody crucial mathematical ideas. We will start with the basic properties of Grassmann spaces to construct the universal vector bundle over them. Through demonstration, we will reveal the internal logic of their role as classifying spaces. Subsequently, by utilizing the theory of characteristic classes, we will prove that the cohomology ring of an infinite-dimensional Grassmann manifold is isomorphic to the integral coefficient polynomial ring generated by the corresponding Chern classes. In the finite-dimensional case, we will introduce the method of Schubert calculus and provide specific calculation methods and results for the structure of its cohomology ring.
Room: 216, East 32 Building.
Time: May 23, 15:00-16:00
Speaker: 汪湜 上海科技大学
Abstract: Given a discrete subgroup H in a higher rank non-compact simple real Lie group G. We show that either H is a lattice in G, or the homological dimension of H is bounded above by (n-1/8r), where n is the dimension of the symmetric space G/K and r is the real rank of G. The proof uses a geometric gradient flow motivated by the Patterson-Sullivan theory and the barycenter map of Besson-Courtois-Gallot. This is joint work with Chris Connell and Ben McReynolds.
Room: 216, East 32 Building.
Time: May 26, 10:30-11:30
Speaker: 洪钰郎
Abstract:Function fields are important examples of global fields. In this talk we will talk about the zeta functions of function fields. After giving basic definitions, we will describe two theorems about such functions. The first one is the about analytic continuation and the second one is about the zeroes these zeta functions. Then we will talk two applications in number theory. The first is the prime distribution. We will show how Riemann hypothesis is related to this problem. Another application is on the class number problem, which gives rise to a famous work of Iwasawa.
Room: 216, East 32 Building.
Time: June 10, 15:00-16:00