Columbia Student Probability Seminar

Spring Semester 2026 Student Probability Seminar

Welcome to the Columbia Student Probability Seminar. We will focus on two main topics, Mixing time for shuffling cards and Stochastic vertex models, based on the following papers one, two, three, and four, five.

Time

Thursday, 5:00–6:00 PM (EST)

Location

Room

First talk

01/29/2026

Schedule of Talks Spring 2026

Date Speaker Content
01/29/2026 Jiyue Zeng We will discuss random transposition shuffling.
02/05/2026 Jiahe Shen We will present the paper "The Szemer\'edi-Trotter theorem over arbitrary field of characteristic zero".
02/12/2026 Jiyue Zeng We discuss the coupling techniques for large k-cycle shuffling.
02/19/2026 Jiahe Shen We explain bounds on character ratios and representation dimensions for large partitions, and compute the Fourier coefficients.
02/26/2026 Jiyue Zeng We will introduce periodic schur process.
03/05/2026 Xinyi Zhang We discussed the construction of strong stationary time for k-cycle shuffling.
03/26/2026 Jiyue and Xinyi We will spend the first half of the session discussing the mixing time of riffle shuffling, and the second half introducing participants' research interests.
04/02/2026 Yiming Tang and Jiyue Zeng We will discuss half-space KPZ fixed point with deterministic initial data and its relation to stationary half-space discrete models.
04/09/2026 Yiming Tang and Xinyi Zhang Practice Talk for Multi-level Directed Landscape. For the second half, we wil briefly discuss the paper "Repeated Averages on Graphs".
04/16/2026 Jiahe Shen The recent breakthrough on the Kakeya conjecture in R^3 is a remarkable result, but its proof is highly nontrivial and draws on techniques from several different areas of mathematics. By contrast, the Kakeya set conjecture in the finite-field and p-adic settings has much simpler proofs. In this talk, I will first introduce Dvir’s proof in the finite-field setting, a landmark application of the polynomial method. I will then discuss Arsovski’s proof in the p-adic setting, which proceeds in a similar spirit.