Finding combinatorial interpretations for the structure constants of Schubert polynomials is a long-standing open problem in algebraic combinatorics. In the case where one of the Schubert polynomials is a Schur…
In this talk we will first briefly review some geometric inverse problems we have studied for the one-dimensional heat, wave and Burgers equations. Then, we will consider a one-dimensional fluid-solid…
In this talk, we will investigate the acoustic transmission eigenvalue problem associated with an inhomogeneous media with a conductive boundary. These are a new class of eigenvalue problems that are…
Quantum computers are physical machines that process information using the principles of quantum mechanics, which in turn is underpinned by linear algebra. The talk will start with a review of…
A number of continuous interacting particle systems can be described as collections of Brownian particles on the real line whose collision dynamics are mediated by the local times associated with…
This talk will begin by constructing a new algebra based on a generalization of the set of relations for Ozsváth-Szabó's bordered Heegaard Floer algebra $B(n,k)$. Then, I will strengthen an…
Matrix computations are ubiquitous in scientific computing and data science. However, many existing methods consume enormous computational resources for solving increasingly large and complex problems. In this talk, I will…
On a Riemannian manifold with boundary, the X-ray transform integrates a function or a tensor field along all geodesics through the manifold. The reconstruction of the integrand of interest from its X-ray transform is the basis of…
Noncrossing partitions and nonnesting partitions are both counted by Catalan numbers. Noncrossing partitions on admit a natural cyclic action of order 2n, induced by the Kreweras complement. Nonnesting partitions admit a natural toggle-based…
How to use mathematics to see inside something that is too large or too precious to be opened up? Would you like to learn about the mathematical theory behind medical…
The trace reconstruction problem asks to reconstruct an unknown n-bit string x given independent random "traces" of x, where a random trace is obtained by first deleting each bit of…
Applications of machine learning (ML) in mixed-integer program (MIP) optimization is an active area of research. The human-designed heuristics used by MIP solvers rely on domain expertise and years of…
The travel time map of a compact length space with a closed measurement set takes any point of the space to the function which measures the distance from this point…
The Schur functions are an important basis of the ring of symmetric functions, and Schur’s Q-functions enjoy many analogous properties as a basis of the subring Gamma. We will begin…
During each 50-minute First Year Research Seminar, two faculty give our new graduate students a short (~20-25 minute), accessible talk about their research or research area. First Year Research Seminar…
In the framework of black-box optimization, I will present new algorithms, based on the stochastic estimation of the gradient via finite differences with structured directions. I will describe their convergence…
Inverse problems are pivotal in a variety of applications, such as target identification, non-destructive testing, and parameter estimation. Among these, the inverse scattering problem in inhomogeneous media poses significant challenges,…