Emmy Noether Room, Estella 1021, Pomona College,

Political scientists forecast elections, not primarily to satisfy public interest, but to validate statistical models used for estimating quantities of scholarly interest. Although scholars have learned a great deal from these models, they can be embarrassingly overconfident: Events that should occur once in 10,000 elections occur almost every year, and even those that should occur […]

A wide variety of medical imaging methods exist for research and diagnostic procedures on the Central Nervous System (CNS), among them Magnetic Resonance Imaging (MRI) and Optical Imaging. Mathematical modeling and simulation contribute significantly to an improved understanding of image data and the intricate transport, diffusion, and metabolic processes in the brain. This is of […]

A Belyĭ pair \bigl( S,\, z(w) \bigr) is a compact, connected Riemann surface S together with a rational function z \colon S \to \mathbb{P}^1(\mathbb{C}) which has at most three critical values \bigl\{ 0,\, 1,\, \infty \bigr\}. The preimage z^{-1}\bigl( \bigr) \subseteq S \hookrightarrow \mathbb{R}^3 is a bipartite graph called a Dessin d'Enfant. When S = \mathbb{P}^1(\mathbb{C}) […]

In multi-armed trials, adaptive designs are a popular way to increase estimation efficiency or identify optimal treatments. Many recent papers have proposed adaptive methods for minimizing the error of unbiased […]

Abstract: I will introduce In-Context Operator Networks (ICON), a framework in which a single neural network learns solution operators for differential equations directly from a few prompted input-output examples at […]

Abstract: Turbulence influences our lives in a multitude of ways, ranging from the mundane (when we stir milk into our coffee) to the spectacular (the formation of galaxies). It is a great achievement of the human intellect that we are able to locate fundamental mechanisms shared by phenomenon with such a dramatic difference in scale […]

Abstract: We study the optimization of Steklov eigenvalues with respect to a boundary density function ρ on a bounded Lipschitz domain. We investigate the minimization and maximization of a Steklov eigenvalue over admissible densities satisfying pointwise bounds and a fixed integral constraint. We establish the existence of optimal solutions and provide structural characterizations: minimizers are […]

Abstract: In this talk, we will describe a well/ill-posedness result for the 2D incompressible Euler equations. We investigate solutions in a setting logarithmically smoother than previously done, in a hope to identify the key dynamics leading to a breakdown of regularity in 2D fluid flow. When order of the logarithmic derivative is sufficiently large one […]

Abstract: This talk presents a regularity criterion for the three-dimensional Navier–Stokes equations based on finitely many observations of the flow. Motivated by data assimilation, we study a nudging algorithm that incorporates coarse spatial measurements through general interpolation operators. We show that suitable conditions on the observed data guarantee global regularity of the associated system and […]

Abstract: The Shapley value is a ubiquitous framework for attribution in machine learning, encompassing feature importance, data valuation, and causal inference. However, its exact computation is generally intractable, necessitating efficient approximation methods. While the most effective and popular estimators leverage the paired sampling heuristic to reduce estimation error, the theoretical mechanism driving this improvement has […]

Abstract: We present a new approach for deriving structure-preserving numerical discretizations of Fokker-Planck equations by establishing a connection between the Fokker-Planck equation and its semi-discrete master equation at the level […]