The goal of this talk is to price American-type financial contracts in the presence of Knightian uncertainty. In particular, instead of choosing a particular probabilistic model to represent the price…
Dense linear systems in large-scale kernel approximation in machine learning, discretization of boundary integral equations in mathematical physics, and low-rank approximation of Schur complements in large sparse matrix factorization often…
As with weather, there is a limit to how far into the future we can accurately forecast the future course of epidemics. Yet, we often need to make plans further into the future than we can reasonably forecast, and in many cases our actions themselves will…
In this talk, I will introduce a novel Riemannian geometric model for wave propagation in gas giant planets. Terrestrial planets and gas giants have one key difference: in gas, density…
In Stanley’s seminal work “Cohen-Macaulay Complexes”, Stanley conjectured that all h vectors of matroid complexes are pure O-sequences. We constructed coparking functions on matroids with extra restrictions and showed that…
In this talk, I shall present a relaxation formula and duality theory for the multi-marginal Coulomb cost that appears in optimal transport problems arising in Density Functional Theory. The related…
We consider weakly compressible flows coupled with a cloud system that models the dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertainties that arise due…
We start by giving a short introduction to geometric inverse problems. Then we present our recent results regarding inverse problems for the minimal surface equation. Minimal surfaces are solutions to…
Quantum hardware has advanced to the point where it is now possible to perform simulations of small physical systems. Although the current capabilities are limited, given the rapid advancement it…
Feasibility models are a powerful approach to many real-world problems where simply finding a point that comes close enough to meeting many, sometimes contradictory demands is enough. In this talk…
Affect (e.g., beliefs, attitudes, emotions) plays a crucial role in mathematics learning, but reliance on verbal and written responses (from surveys, interviews, etc.) can limit students’ expression of their affective…
In this talk we present both numerical analysis and experiments to study a few basic computational issues in practice: (1) the numerical error one can achieve given a finite machine…
Consider a dense Erdös-Rényi random graph with parameters n and p, with p fixed in (0,1). Let H_n(p) be the hitting time between two distinct vertices: run simple random walk from…
PyOED is a highly extensible scientific package that enables developing and testing model-constrained optimal experimental design (OED) for inverse problems. Specifically, PyOED aims to be a comprehensive Python toolkit for…
This talk will focus on point-cloud data, their analysis and biological applications in which they naturally arise. In particular, I will introduce "optimal transport", which has evolved as one of…
Consider the affine Lie algebra $\mathfrak{g}$ associated with the simple Lie algebra $sl(n)$ consisting of $n\times n$ trace zero matrices over the field of complex numbers. For every dominant integral…
A hollow vortex is a region of constant pressure bounded by a vortex sheet and suspended inside a perfect fluid; we can think of it as a spinning bubble of…
Physics-Informed Neural Networks (PINNs) have received much attention recently due to their potential for high-performance computations for complex physical systems, including data-based computing, systems with unknown parameters, and others. The…