I am co-organizing a virtual Probability Seminar with Wei-Kuo Chen and Arnab Sen at University of Minnesota for
the Spring 2025 semester. Please email me to get the Zoom link for the seminar series.
The seminar is held on Fridays at 2:30pm (ET), unless otherwise noted below.
| 09/12/2025 | Wei-Kuo Chen (U Minnesota) |
| Title: On the fitness landscape of the NK model. | |
| Abstract: The NK model, introduced by Kauffman, Levin, and Weinberger, is a random field used to describe the fitness landscape of certain species with N genetic loci, each interacting with K others. It is expected to capture rugged landscapes in some evolutionary systems and has been instrumental in studying evolutionary dynamics through adaptive walks. Earlier literature has been focused on the case K being a fixed positive integer and used tools from Ergodic and Markov theory. In this talk, I will present some new results concerning the fitness landscape in the NK model under the regime that K/N is approximately α ∈(0,1]. These include the explicit formulas for the free energy and maximum fitness, overlap gap properties, and multiple peak structure of the level set near the maximum fitness, and the existence of evolutionary paths of nearly maximum fitness. Along the way, I will discuss the implications of our results in relation to evolution dynamics and explain how spin glass theory is of great use in our study. Based on a joint work with S. Tang. | |
| 09/19/2025 | Gabriel Raposo (UC Berkeley) |
| Title: Fluctuations of random standard Young Tableaux. | |
| Abstract: We will introduce the Young generating function and use it to characterize the law of large numbers and the central limit theorem behaviors for random partitions. As an application of these results, we present a framework to obtain conditional Gaussian Free Field fluctuations for height functions associated with random standard Young tableau. To prove these results we develop algebraic formulas for operators on the Gelfand–Tsetlin algebra of the symmetric group. | |
| 09/26/2025 | Grigory Terlov (UNC) |
| Title: Percolation on nonunimodular graphs. | |
| Abstract: Percolation theory has traditionally been developed on unimodular transitive graphs (i.e., graphs with symmetries similar to Cayley graphs). I will present recent progress in extending the theory to the nonunimodular setting. In particular, I will discuss how properties of the automorphism group of the graph, such as amenability, reflect in percolation processes, and present generalizations of several classical unimodular results to the setting of all transitive graphs. Perhaps unexpectedly, these advances have been motivated or even enabled by developments in measured group theory. The talk will be accessible to a broad audience, with no prior familiarity with the topic assumed. | |
| 10/03/2025 | Evan Sorensen (Columbia) |
| Title: Invariant measures and shocks in the KPZ fixed point. | |
| Abstract: I will discuss a recent preprint, joint with Alex Dunlap, where we show the existence of a family of invariant measures from the perspective of a shock in the KPZ fixed point. Each measure can be described as the sum of a Brownian motion and an independent Bessel-3 process with drift. We show how these measures also appear as the L \to\infty limit of the conjectural open KPZ fixed point measures previously considered in the work of Barraquand and Le Doussal and in the work of Barraquand, Corwin, and Yang, after recentering by an appropriately-defined shock location. Furthermore, we classify the extremal invariant measures for the KPZ fixed point with respect to the standard recentering at 0. To do so, we describe the limiting fluctuations of shocks for three special cases of initial data. | |
| 10/17/2025 | Brice Huang (Stanford) |
| Title: Capacity threshold for the Ising perceptron. | |
| Abstract:We show that the capacity of the Ising perceptron is with high probability upper bounded by the constant α ≈ 0.833 conjectured by Krauth and Mézard, under the condition that an explicit two-variable function S(λ1,λ2) is maximized at (1,0). The earlier work of Ding and Sun proves the matching lower bound subject to a similar numerical condition, and together these results give a conditional proof of the conjecture of Krauth and Mézard. | |
| 10/31/2025 | Konstantinos Zampetakis (TU Dortmund) |
| Title: TBA | |
| Abstract: TBA | |
| 11/07/2025 | Kihoon Seong (Cornell / SLMath) |
| Title: TBA | |
| Abstract: TBA | |