山大数论讨论班

2026年春季学期

中心校区明德楼 C704 & 洪家楼校区

组织者：山大数论组

讨论班着重于数论中的新进展。报告人为校内外学者和学生。欢迎推荐报告。

报告信息（摘要和往年报告信息见列表下方）

• 2026-03-05，15:00-16:00   徐文强   Courant Institute   

  题目：Arithmetic aspects of random multiplicative functions

  摘要：

  地点：明德楼C704

• 2026-03-19，15:00-16:00   Ezra Waxman   Afeka College of Engineering

  题目：Lattice Points in Thin Sectors

  摘要：On the circle of radius R centred at the origin, consider a ``thin'' sector about the fixed line y = \alpha x with edges given by the lines y = (\alpha \pm \epsilon) x, where \epsilon = \epsilon_R \rightarrow 0 as R \to \infty. We discuss an asymptotic count for S_{\alpha}(\epsilon,R), the number of integer lattice points lying in such a sector, and moreover present results concerning the variance of such lattice points across sectors.

  地点：明德楼C704

• 2026-03-24，9:30-10:30   贺宇昕   清华大学

  题目：Uniform spectral gaps for random hyperbolic surfaces with not many cusps

  摘要：We investigate uniform spectral gaps for Weil-Petersson random hyperbolic surfaces with not many cusps. We show that if $n=O(g^\alpha)$ where $\alpha\in \left[0,\frac{1}{2}\right)$, then for any $\epsilon>0$, a random cusped hyperbolic surface in $\mathcal{M}_{g,n}$ has no eigenvalues in $\left(0,\frac{1}{4}-\left(\frac{1}{6(1-\alpha)}\right)^2-\epsilon\right)$.  If $\alpha$ is close to $\frac{1}{2}$, this gives a new uniform lower bound $\frac{5}{36}-\epsilon$ for the spectral gaps of Weil-Petersson random hyperbolic surfaces. The major contribution of this work is to reveal a critical phenomenon of ``second order cancellation". This talk is based on a joint work with Yunhui Wu and Yuhao Xue.

  地点：明德楼 C704

• 2026-03-24，10:40-11:40   张皓皓   清华大学

  题目：Short geodesics and multiplicities of eigenvalues of hyperbolic surfaces

  摘要：We obtain upper bounds on the multiplicity of Laplacian eigenvalues for closed hyperbolic surfaces in terms of the number of short closed geodesics and the genus g. For example, we show that if the number of short closed geodesics is sublinear in g, then the multiplicity of the first eigenvalue is also sublinear in g. This makes new progress on a conjecture by Colin de Verdière in the mid 1980s. This talk is based on a joint work with Xiang He and Yunhui Wu.

  地点：明德楼 C704

• 2026-04-21，15:00-16:00   Steve Lester   King's College London

  题目：

  摘要：

  地点：明德楼 C704

山大数论讨论班

星期三，15:00-16:00，2025年秋季学期

中心校区明德楼 C704 & 洪家楼校区

组织者：山大数论组

讨论班着重于数论中的新进展。报告人为校内外学者和学生。欢迎推荐报告。

报告信息（摘要和往年报告信息见列表下方）

• 2025-09-17，杨一帆   台湾大学

  题目：

  摘要：

  地点：洪家楼校区1号楼

• 2025-09-24，杨一帆   台湾大学

  题目：

  摘要：

  地点：洪家楼校区

• 2025-10-29，华晟昊

  题目：Distribution of automorphic forms and families of $L$-functions

  摘要：Berry suggested that the eigenfunctions of chaotic systems can be modeled as random waves. It is widely believed that the moments of a normalized eigenfunction should coincide with those of a Gaussian distribution. In this talk, we will discuss a conjecture concerning the statistical independence in the joint distribution of Hecke--Maass cusp forms, along with two conditional results, based on joint work with Bingrong Huang and Liangxun Li.

  In one case, our proof relies on a phenomenon in which the moments of a ``mixed'' family of $L$-functions can be compared with those of a ``pure'' family of $L$-functions. This naturally raises the question: what constitutes a general family of $L$-functions?

  In the second part of the talk, I will introduce the toroidal families introduced by Fouvry, Kowalski, and Michel, which are defined via subgroups of characters. In ongoing joint work with Michel, we have developed a fundamental matrix framework that facilitates computations in the general setting. We illustrate this framework through examples spanning various ranks, including both low- and high-rank cases.

  地点：明德楼 C704

• 2025-12-15，程创勋   南京大学

  题目：On the splitting fields of principal homogeneous spaces for elliptic curves

  摘要：Let K/Qp be a finite extension and E/K be an elliptic curve. For a principal homogenous space C of E/K, the period of C is defined as the order of C as an element in the Weil-Châtelet group WC(E/K). A finite extension L/K is called a splitting field of C if C(L) is nonempty. It is known that when E/K has good reduction and the period of C is coprime to p, the extension L/K splits C if and only if the period of C divides the ramification index eL/K. The case in which the period of C is a power of p is more subtle. In this talk, I will present our recent work on this question for elliptic curves over Qp with good supersingular reduction and the period-index distribution problem.

  地点：明德楼 C704

• 2025-12-17，彭云剑   清华大学

  题目：Rankin--Selberg $L$-函数的 Weyl 界

  摘要：随着Rankin--Selberg $L$-函数的亚凸界问题已基本得到解决，Weyl界的研究成为该领域新的核心目标。本报告将介绍 Weyl 界的若干近期研究进展，并阐述我们借助相对迹公式与 adelic Voronoi求和公式，在一类新型Weyl界估计方面取得成果。

  地点：明德楼 C704

• 2025-12-24，叶李源   清华大学

  题目：Stationary phase analysis for analytic newvectors and applications to the subconvexity problem

  摘要：In this talk, I will discuss an extension of the results of Michel-Venkatesh and Hu-Michel-Nelson, establishing an upper bound for triple product and Rankin-Selberg L-functions of the form
  $$L(\pi_1\otimes\pi_2\otimes\pi_3,\frac{1}{2})\ll_{\pi_3,\epsilon}C(\pi_1\otimes\pi_2)^{\frac{1}{2}+\epsilon}\left(\frac{C(\pi_1\otimes\pi_2)}{C(\pi_2\otimes\pi_2)}\right)^{-\delta}$$
  in the spectral aspect, allowing conductor dropping. In particular, we obtain a subconvexity bound when $\pi_1\otimes\pi_2$  stays uniformly away from QUE-like case.

  地点：明德楼 C704

往年报告：

• 2025年春季报告
  

• 2024年秋季报告    2024年春季报告   
  

• 2023年秋季报告    2023年春季报告

• 2022年秋季报告 2022年春季报告

• 2021年秋季报告 2021年春季报告

• 2020年秋季报告 2020年春季报告

Contact us at: brhuang "at" sdu dot edu dot cn,   Office: Mingde C701,   Tel: 883-69786