| Date | Speaker | Title | Abstract |
|---|---|---|---|
| September 11, 2026 | Chamsol Park, University of Rochester | Uncertainty Principles and Singular Potentials on Compact Manifolds | In this talk, we will briefly review uncertainty principles developed previously for homogeneous manifolds or discrete cases, and will discuss how we can extend these results to more general compact Riemannian manifolds without boundary. This is joint work with Alex Iosevich. |
| September 18, 2026 | Zane Li, North Carolina State University | Mizohata-Takeuchi Type Inequalities for Moment Curves |
In an online talk from 2022, Larry Guth considered the Mizohata-Takeuchi conjecture for the parabola and demonstrated that any improvement beyond a R^{1/3} loss needed tools beyond wavepackets and Fourier decoupling. In 2023, Tony Carbery, Marina Iliopoulou and Hong Wang attained this loss (in the case of the parabola and the paraboloid in general) as a consequence of refined decoupling.
In joint work with Tony Carbery, Yixuan Pang, and Po-Lam Yung, we generalize this work to the moment curve, thus proving a version of the Mizohata-Takeuchi conjecture for "well-curved" curves with a loss that matches the numerology of Carbery-Iliopoulou-Wang for the parabola. In this talk, we will discuss the history of and progress towards the Mizohata-Takeuchi conjecture, refined decoupling, and some aspects of the proof I found quite interesting. |
| September 25, 2026 | Jeffrey Kuan, University of Rochester | Recent Progress in Fluid-Structure Interaction |
In this talk, I will give an overview of the mathematical theory of fluid-structure interaction and discuss some recent results. Fluid-structure interaction describes the coupled dynamics of a fluid flow interacting with an elastic or deformable structure, with applications ranging from mechanical engineering to biomedical engineering.
I will first discuss some of the mathematical challenges that arise in fluid-structure interaction problems and describe approaches for studying these systems. These are moving-boundary problems involving coupled partial differential equations for the fluid and the elastodynamics of the structure. The resulting systems are highly nonlinear systems, where the fluid domain evolves in time and is not known a priori. I will then discuss recent progress in fluid-structure interaction, including the analysis of stochastically forced fluid flows interacting with elastic structures, as well as well-posedness results for problems describing a fluid flow interacting with a poroelastic medium. This is joint work with Suncica Canic (UC Berkeley), Krutika Tawri (UW), and Boris Muha (University of Zagreb). |
| September 28, 2026 (special time and place: 11:50-12:50, Goergen 108) | Mark Iwen, Michigan State University | Low-Distortion Embeddings of Submanifolds of $R^n$: Lower Bounds, Faster Realizations, and Terminal Embeddings |
Let M be a smooth submanifold of $R^n$ equipped with the Euclidean(chordal) metric. This talk will consider the smallest dimension, m, for which there exists a bi-Lipschitz function $f:M \to R^m$ with bi-Lipschitz constants close to one. We will begin by presenting a bound for the embedding dimension m from below in terms of the bi-Lipschitz constants of f and the reach, volume, diameter, and dimension of $M$. We will then discuss how this lower bound can be applied to show that prior upper bounds by Eftekhari and Wakin on the minimal low-distortion embedding dimension of such manifolds using random matrices achieve near-optimal dependence on dimension, reach, and volume (even when compared against nonlinear competitors). Using this as motivation, we will then discuss non-linear so-called ''terminal embeddings" of sets which allow for powerful extensions of the famous Johnson-Lindenstrauss Lemma beyond what any linear map can achieve. In addition to nearly preserving all distances within a set, these extensions also nearly preserve all distances from outside the set to elements in the set in a lower-dimensional space, all while remaining continuous! If you haven't seen them before, come and meet them - you won't regret it.
This talk will draw on joint work with various subsets of Simone Brugiapaglia (Concordia U), Rafael Chiclana Vega (NYU Abu Dhabi), Tim Hoheisel (McGill), Benjamin Schmidt (MSU), and my former students Mark Roach & Arman Tavakoli. |
| October 9, 2026 (jointly with the Probability seminar; special time and place: 15:00-16:00, Hylan 1106A) | Semyon Dyatlov, Massachusetts Institute of Technology | Fractal Uncertainty Principle and Projection Theory |
Fractal uncertainty principle (FUP) is an estimate on the $L^2$ operator norm of $1_X B_h 1_Y$ where $X,Y$ are fractal sets down to some small scale $h$ and $B_h$ is a unitary operator whose integral kernel oscillates at wave length $h$. This has applications to quantum chaos, including spectral gaps for convex co-compact hyperbolic surfaces. Many FUP results are available, typically reducing the case of general $B_h$ to the Fourier transform.
In this talk I will give a new FUP with a reasonably large exponent for $1/2$-dimensional sets $X,Y$, relying on the difference between the operator $B_h$ used for hyperbolic surfaces and the Fourier transform. The key ingredients come from projection theory. Joint work with Alex Cohen, and some help from AI. |
| November 13, 2026 | Krutika Tawri, University of Washington |