Columbia University · Department of Mathematics

Student Probability Seminar

Fall 2026

The Student Probability Seminar is a forum for graduate students to present and discuss topics across probability theory and related areas. Talks may cover random matrices, interacting particle systems, stochastic processes, random graphs, statistical mechanics, integrable probability, and connections between probability and other areas of mathematics.

When
Thursdays, 4:15–5:15 PM
Location
Mathematics 528
Semester
Fall 2026

Organizers

Jiyue Zeng
Xinyi Zhang
Jiahe Shen

Schedule of Talks

Date Speaker Title and Abstract
September 10, 2026 Jiahe Shen
Practice talk
p-adic Eigenvalue Statistics and Universality
Random matrix models play a central role in arithmetic statistics, from the Katz-Sarnak philosophy for zeros of L-functions to the Cohen-Lenstra heuristics for class groups. I will discuss an analogous non-archimedean picture involving random matrices over the p-adic integers. The main questions concern local eigenvalue statistics, including correlation functions for eigenvalues in finite extensions of Qp, and the extent to which these statistics are universal beyond the Haar model. I will also explain how resultant distributions and random cokernels provide a route to proving universality, and how these results connect to predictions for zeros of p-adic L-functions.
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The schedule will be updated as speakers and topics are confirmed.