报告时间：2026年5月14日（周四）下午 16:00-17:00
报告地点：苏州大学天赐庄校区精正楼306
报告人：吴涵 副教授，北航杭州国际创新研究院
报告摘要：
The prime geodesic theorems (PGT) are analogues of the prime number theorem (PNT), in which we count the primitive closed geodesics in Γ\H instead of prime numbers. Here Γ < PSL_2(R) is a lattice, and H is the Poincaré upper half plane. The race is about the upper bound of the error term as O(x^θ). In the setting of co-compact lattices constructed from quaternion algebras, the record is kept by Koyama for full level subgroups at Luo–Sarnak's level θ = 7/10. Koyama's method is an exploitation of the Jacquet–Langlands correspondences on the spectral side.
We generalize Koyama's 7/10 bound to the principal congruence subgroups for quaternion algebras. Our method avoids the spectral side of the Jacquet–Langlands correspondences, and relates the counting function directly to those for the principal congruence subgroups of Eichler orders of square-free level. We shall discuss the possibility and difficulty for further generalization to other congruence subgroups.
This is a joint work with three undergraduate students (Chenhao Tang, Jie Yang and Wenyan Yang) during the event of the 2025 summer school entitled "Algebra and Number Theory" held at the Chinese Academy of Sciences.
报告人简介：
吴涵，本科和硕士分别毕业于清华大学和巴黎综合理工，博士毕业于瑞士洛桑联邦理工(EPFL)，导师为Philippe Michel。曾就职于苏黎世联邦理工、匈牙利Rényi数学研究所、伦敦玛丽女王大学、中国科学技术大学，现为北航杭州国际创新研究院副教授。研究方向为解析数论与自守表示，特别关注L-函数亚凸界问题及其在解析数论相关问题中的应用，在GAFA, Compos. Math., TAMS等杂志发表论文十余篇。
邀请人：董自康