Fall 2025
August 27, 2025, 4:00–5:00pm, EH4088
Speaker: Félix Parraud (Queen's University)
Title: A new approach to computing matrix integrals
Abstract: This talk will focus on a new strategy introduced in the last few years which has turned out to be a very useful tool to study the asymptotic behaviour of random matrices and compute matrix integrals. It relies on the theory of free stochastic calculus developed by Biane and Speicher in the late '90s. I will explain the heuristic behind those results, as well as list a few of them. In particular I will explain how it was used to deduce a proof of a conjecture on the strong convergence of a family of random matrices which implies the Peterson–Thom conjecture thanks to the work of Ben Hayes.
September 3, 2025, 4:00–5:00pm, EH4088
Speaker: Sayan Das (University of Chicago)
Title: Large Deviation Principle for the Directed Landscape
Abstract: The directed landscape is a random directed metric on the plane that arises as the scaling limit of classical metric models in the KPZ universality class. In this talk, I will discuss a functional large deviation principle for the entire random metric and mention certain interesting features of the underlying rate function. If time permits, I will also discuss some applications of our results. Based on a joint work with Duncan Dauvergne and Balint Virag.
September 17, 2025, 4:00–5:00pm, EH4088
Speaker: Zhipeng Liu (University of Kansas)
Title: Multipoint distributions of the KPZ fixed point with compactly supported initial conditions
Abstract: The KPZ fixed point is a universal limiting space-time random field for the Kardar-Parisi-Zhang universality class. While the joint law of the KPZ fixed point at a fixed time has been studied extensively, the multipoint distributions of the KPZ fixed point in the general space-time plane are much less well understood. More explicitly, formulas were only available for the narrow wedge initial condition [JR21,Liu22] and the flat initial condition [Liu22] for the multipoint distributions, and the half-Brownian and Brownian initial conditions [JR22, Rah25] for the two-point distributions.
In this talk, I will talk about my recent work with Yuchen Liao in which we obtained the first formula for the space-time joint distributions of the KPZ fixed point with general initial conditions of compact support. The formula is obtained through taking 1 : 2 : 3 KPZ scaling limit of the multipoint distribution formulas for the totally asymmetric simple exclusion process (TASEP). A key novelty is a probabilistic representation, inspired by [MQR21], of the kernel encoding the initial condition for TASEP, which was first defined through an implicit characterization in [Liu22]. Moreover, we also verify that the equal time degenerated version of our formula matches the path integral formula in [MQR21] for the KPZ fixed point.
This is a joint work with Yuchen Liao (University of Science and Technology of China).
September 24, 2025, 4:00–5:00pm, EH4088
Speaker: Xincheng Zhang (Caltech)
Title: TBA
Abstract: TBA