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    2025年自守形式与表示研讨会

    2025-12-12   至   2025-12-15


    2025-12-12 签到
    2025-12-13 上午会场 主持人: 徐钊           厦门大学海韵园实验楼S106
    09:00-09:50 林永晓
    山东大学    		 Levinson's method with a short mollifier 摘要
    09:50-10:10                      茶歇
    10:10-11:00 任汝飞
    复旦大学    		 The Ghost Conjecture on Irreducible Local Representations 摘要
    11:10-12:00 柴劲松
    安徽工程大学    		 On parabolic induction and Jacquet module over $p$-adic group 摘要
    下午会场 主持人: 冯泳祺           厦门大学海韵园实验楼S106
    14:30-15:20 罗才华
    香港中文大学（深圳）    		 Socle Filtration and Intertwining Operator 摘要
    15:20-15:40                      茶歇
    15:40-16:30 田乙胜
    哈尔滨工业大学    		 On cohomological invariants of algebraic groups 摘要
    16:40-17:30 佘东明
    北京雁栖湖应用数学研究院    		 Coperiods and central symmetric cube $L$-values 摘要
    2025-12-14 上午会场 主持人: 李加宁           厦门大学海韵园实验楼S106
    09:00-09:50 王善文
    中国人民大学    		 The $p$-adic Eichler-Shimura map 摘要
    09:50-10:10                      茶歇
    10:10-11:00 蒋玉蛟
    山东大学    		 On Hypothesis H of Rudnick and Sarnak 摘要
    11:10-12:00 张神星
    合肥工业大学    		 含非同余数因子的非同余数 摘要
    下午会场 自由讨论
    2025-12-15 离会

    摘要

    林永晓 - Levinson's method with a short mollifier

    This is joint with Brian Conrey, David Farmer, Chung-Hang Kwan, and Caroline Turnage-Butterbaugh. When studying the zeros of Riemann zeta function at a height $T$ up the critical strip one often multiplies zeta by a Dirichlet polynomial, called a mollifier, of length $T^\theta$ before averaging in order to neutralize the irregularities of zeta. Levinson in his 1974 Advances paper famously proved that at least 1/3 of the zeros of zeta are on the critical line, by using a mollifier of length $T^\theta$ with $\theta<1/2$. Significant efforts in the literature have been devoted to refine and optimize Levinson's mollifer. We prove that Levinson's method, as modified by Conrey, will in fact produce a positive proportion of critical zeros, regardless how short the mollifier is.

    任汝飞 - The Ghost Conjecture on Irreducible Local Representations

    The Ghost Conjecture was jointly proposed by Bergdall and Pollack. When the local representation is reducible and generic, this conjecture has been resolved by Liu Ruochuan, Xiao Liang, Zhao Bin, and Nha Truong. In this talk, I will present our progress on the Ghost Conjecture under the condition of irreducible representations, particularly focusing on the construction of ghost series in this case. This is a joint work with Zhao Bin.

    柴劲松 - On parabolic induction and Jacquet module over $p$-adic group

    In this talk, we will use tensor product with appropriate bimodules over Hecke algebras to discuss parabolic induction and Jacquet module. We will also discuss a similar construction in local theta correspondence.

    罗才华 - Socle Filtration and Intertwining Operator

    Analogous to the celebrated Birch and Swinnerton-Dyer conjecture (BSD conjecture for short), relating the rank of rational points of an elliptic curve and the vanishing order of the corresponding $L$-functions, we uncover a local BSD-type phenomenon linking the lengths of socle filtrations of an induced representation to the vanishing orders of the associated normalized standard intertwining operator, i.e., local $L$-functions.

    田乙胜 - On cohomological invariants of algebraic groups

    In this talk, we first recall definitions and basic properties of cohomological invariants of algebraic groups. Subsequently, we use cohomological invariants to construct a so-called versal torsor. Finally, we introduce a comparison of cohomological obstructions via versal torsor over $p$-adic function fields. This is based on a joint work in progress with CAO Yang (曹阳).

    佘东明 - Coperiods and central symmetric cube $L$-values

    The deep and intrinsic connections between period integrals and special values of automorphic $L$-functions form a central theme in modern automorphic representation theory. In this talk, I will discuss how the central symmetric cube $L$-values of automorphic representations of $\mathrm{GL}(2)$ are related to certain coperiod integrals associated to the cubic Kazhdan-Patterson covers of $\mathrm{GL}(2)$. I will formulate the corresponding GGP-type conjecture and discuss the Ichino-Ikeda type formula for Eisenstein periods. This is a joint work with Li Cai and Yangyu Fan.

    王善文 - The $p$-adic Eichler-Shimura map

    Using the CdR conjecture for modular forms, we give an explicit description of the $p$-adic Eichler-Shimura map. This talk is based on joint work with Pierre Colmez.

    蒋玉蛟 - On Hypothesis H of Rudnick and Sarnak

    The generalized Ramanujan conjecture (GRC) is one of the foundational problems in modern number theory. Hypothesis H can often substitute for the GRC in analytic applications. In this talk, we will discuss our work that proves this hypothesis, establishing it in its full generality and with a bound that is stronger than its original formulation. This result has a number of immediate applications to other central problems in analytic number theory.

    张神星 - 含非同余数因子的非同余数

    我们将回顾非同余数 $n$ 对应的同余椭圆曲线 $E_n:y^2=x^3-n^2x$ 的2-Selmer 秩达到第二小情形的已知结果, 并介绍新的构造此类非同余数的方法.