Fall 2025
November 5, 2025, 4:00–5:00pm, EH4088
Speaker: Will Burstein (University of Rochester)
Title: Lambda(p) Style Bounds in Orlicz Spaces Close to L_2
Abstract: In 2022, Ryou proved a variant of Bourgain's celebrated Lambda(p) Theorem for Zygmund spaces for p > 2. Iosevich and Mayeli stated the p=2 case as an open problem in their 2025 (ACHA) paper and stated that if solved, it would have applications to signal recovery. Limonova made some progress on the latter problem in 2023. In our work, we improve Limonova's result by a logarithmic factor, and we show that the result cannot be improved using the set of probabilistic tools commonly used to solve this type of problem.
Our work is an application of a general framework from Talagrand's textbook (2021). A large component of the talk will be to advocate for the use of frameworks, such as the latter, as a possible problem-solving strategy where our work is a case study.
November 6 (Thursday!), 2025, 4:00–5:00pm, EH4088
Speaker: Axel Saenz Rodriguez (Oregon State University)
Title: Bethe Ansatz and dynamics of interacting particle systems
Abstract: We present a method, using the Bethe Ansatz, to produce exact dynamics for a collection of interacting particle systems. The Bethe Ansatz was introduced in 1931 by Hans Bethe to find eigenvectors and eigenvalues for the generator of a one-dimensional quantum spin system, which is also the setting for this talk. While the Bethe Ansatz proved to be an effective computational tool, providing deep insight into quantum spin chains, it lacked many rigorous theoretical guarantees for many years. There has been much elucidating mathematical activity over the decades to understand the hidden symmetries and analytical consequences of the Bethe Ansatz, and many theoretical questions have been answered. In this talk, we address how to obtain exact dynamics for the Heisenberg-Ising XXZ spin-1/2 periodic chain using the Bethe Ansatz. We provide precise formulas to take a linear combination of the eigenvectors from the Bethe Ansatz and obtain exact dynamics. The formulas presented have been rigorously confirmed for some special cases and the general case has only been confirmed numerically.
This talk is aimed at a general math audience with no special background needed beyond linear algebra and analysis.