地点：数学高等研究院报告厅

主讲人：江迪华教授（明尼苏达大学）

摘要:This lecture series offers an introductory course on the descent method and automorphic integral transforms. These methods provide explicit constructions of irreducible cuspidal automorphic representations of classical groups from certain irreducible automorphic representations of general linear groups. A central theme is the realization of endoscopic correspondences for classical groups through automorphic integral transforms, interpreted in the framework of Arthur’s classification of the discrete spectrum of square-integrable automorphic forms.

Special Lectures on June 12 (Thursday)

时间：14:00-14:50

报告人：唐国栋

题目：Classification of exceptional hyperspherical data and their duals

摘要：The recent joint work of Ben-Zvi, Sakellaridis and Venkatesh (BZSV) proposed a duality of the relative Langlands problem though the concept of hyperspherical data (G, H, \iota, S). This talk will focus on the construction of its dual data and the joint work of Wan, Zhang, and myself on the exceptional case though G = F_4. 

时间：15:00-15:50

报告人：罗嘉盛

题目：Period integrals associated to dual of strongly tempered hyperspherical variety

摘要: Recent work of Mao, Wan and Zhang have provided a complete list of strongly tempered hyperspherical varieties and they proposed some new period integrals. In this paper, I will present some new period integrals associated to dual of strongly tempered distinguished polarised hyperspherical varieties and discuss the L-functions these integrals represent, as examples of the Relative Langlands Duality.

时间：16:00-16:50

报告人：罗智康 

报告: Arithmetic Wavefronts Coincide with Associated Varieties for Discrete Series of Real Classical Groups

摘要: This report establishes the coincidence between the two invariants for discrete series of real classical groups. We first parametrize discrete series using both Langlands parameters and Harish-Chandra parameters, reviewing their correspondence. Algorithms for computing arithmetic wavefront sets and associated varieties are then reviewed. The central result is a proof of the equivalence, confirming their fundamental relationship in the representation theory of real reductive groups.

Special Lectures on June 17 (Tuesday)

时间：14:00-14:50

报告人：李兆林

题目：The uniqueness of the Ginzburg-Rallis model

摘要: The Ginzburg-Rallis model was introduced by Ginzburg and Rallis to conjecturally characterize the non-vanishing of the central value of the exterior cubic L-functions. In the adjoint work with Dihua and Guodong, we extend the strategy of Dihua Jiang, Binyong Sun, and Cheng-Bo Zhu to the non-Archimedean case to complete the uniqueness starting from the work of Chufeng Nien.

时间：15:00-15:50

报告人：席国栋

题目：On the Braverman–Kazhdan–Ngô Triples

摘要：The Braverman–Kazhdan proposal aims to provide a systematic construction of Fourier transforms and Schwartz spaces with an associated Poisson summation formula, in order to deduce the analytic properties of L-functions. In this talk, I will present the construction of the Braverman–Kazhdan–Ngô triple, which plays a central role in this framework.