Fall 2025
September 24, 2025, 4:00–5:00pm, EH4088
Speaker: Xincheng Zhang (Caltech)
Title: TASEP and KPZ Fixed Point in Half-space
Abstract: The Kardar–Parisi–Zhang (KPZ) fixed point is the universal scaling limit for a broad class of one-dimensional stochastic growth models, including the totally asymmetric simple exclusion process (TASEP). In this talk, I will present the transition probability of TASEP in half-space starting with a general deterministic initial condition. Applying the 1:2:3 KPZ scaling limit to this result yields an explicit formula for the half-space KPZ fixed point. Finally, we will discuss a connection between the half-space KPZ fixed point and a system of integrable coupled PDEs.
October 1, 2025, 4:00–5:00pm, EH4088
Speaker: Nikhil Bansal (University of Michigan)
Title: On Beck–Fiala and Komlós Conjectures
Abstract: A conjecture of Komlós states that the discrepancy of any collection of unit vectors is O(1), i.e., for any matrix A with unit columns, there is a vector x with -1,1 entries such that |Ax|_\infty = O(1). The related Beck–Fiala conjecture states that any set system with maximum degree k has discrepancy O(k^{1/2}).
I will describe an O((log n)^{1/4}) bound for the Komlós problem, improving upon an O((log n)^{1/2}) bound due to Banaszczyk, using the framework of discrete Brownian motion guided by semidefinite programs. Time permitting, I will sketch how these ideas can be used to resolve the Beck–Fiala conjecture for k >=(log n)^2.
October 22, 2025, 4:00–5:00pm, EH4088
Speaker: Antonios Zitridis (University of Michigan)
Title: TBA
Abstract: TBA
October 29, 2025, 4:00–5:00pm, EH4088
Speaker: Alexander Volberg (MSU)
Title: Quantum Remez inequality for fast query learning of d-local Hamiltonians
Abstract: How to learn a 2^n times 2^n matrix by asking approximately log n questions? Of course there is no way. But if we know the matrix is a d-local Hamiltonian, then this becomes possible by a recent result of Lars Becker, Joe Slote, Ohad Klein, myself, and Haonan Zhang. The result is a certain dimension-free discrete Remez inequality. Its proof is probabilistic.