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.
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. |