Disordered systems are mathematical models (typically of the physical world) that are governed by random variables. These models have offered insights into a diverse array of research problems, and have…
Gibbs measures are ubiquitous in statistical mechanics and probability theory. In this talk I will discuss two types of classes of Gibbs measures – random line ensembles and triangular particle…
In the study of disordered quantum systems, it is believed that a strong dichotomy should occur between two phases: a delocalized (or conducting) phase and a localized (or insulating) phase.…
A classical result due to Dobrushin (1956) yields the central limit theorem for partial sums of functionals of inhomogeneous ("sufficiently contracting'') Markov chains. In the talk we will restrict to…
We will introduce both finite and infinite-type surfaces and study their collections of symmetries, known as mapping class groups. The study of the mapping class group of finite-type surfaces has played…
I will present problems arising from biochemical reaction networks, optimization, computer science, and complexity theory. These problems share the following characteristics: 1) they can be modeled by multivariate polynomials, 2) they…
The topology of smooth manifolds is governed largely by geometry in low dimensions and by algebraic topology in high dimensions. The phase transition occurs in dimension four, leading to "exotic" phenomena…
In this talk, I will discuss how incorporating geometric information into classical learning algorithms can improve their performance. The main focus will be on optimal mass transport (OMT), which has evolved as a…
Qualitatively, a tipping point in a dynamical system is when a small change in system inputs causes the system to move to a drastically different state. The discussion of tipping points…
In many recent works, analysis and number theory go beyond working side by side and team up in an interconnected back and forth interplay to become a powerful force. Here I describe two distinct meetings of the pair, which result in sharp counts for equilateral triangles in Euclidean…
Speaker: Lisa Fauci, Professor of Mathematics, Tulane University Abstract: In the past decade, the study of the fluid dynamics of swimming organisms has flourished. My research has been centered on…
The stochastic processes of evolution have generated DNA, RNA, and protein sequences. These sequences determine how these entities chemically interact with themselves and each other, form physical structures, and functionally…
We define vertex-colourings for edge-coloured digraphs, which unify the theory of P-partitions and proper vertex-colourings of graphs. Furthermore, we use our vertex-colourings to define generalized chromatic functions, which merge the chromatic symmetric and…
Stochastic fluctuations drive biological processes from particle diffusion to neuronal spike times. The goal of this talk is to use a variety of mathematical frameworks to understand such fluctuations and…
Machine learning (ML) has achieved unprecedented empirical success in diverse applications. It now has been applied to solve scientific problems, which has become an emerging field, Scientific Machine Learning (SciML).…
In this talk, we study an exploration version of continuous time expected utility maximization problem with reinforcement learning. It is shown that the optimal feedback policy is Gaussian. We then…
The concept of multidegrees provides the right generalization of the degree of a projective variety to a multiprojective setting. The study of multidegrees goes back to seminal work by van…
Recent years have witnessed tremendous progress in developing and analyzing quantum computing algorithms for quantum dynamics simulation of bounded operators (Hamiltonian simulation). However, many scientific and engineering problems require the…
Many problems in scientific computing require minimizing nonsmooth optimization problems. In many applications, it is common to minimize the sum of a smooth nonconvex function and a nonsmooth convex function.…
A hyperplane arrangement is a union of codimension one linear spaces. These simple objects provide fertile ground for interactions between combinatorics, algebra, algebraic geometry, topology, and group actions. The combinatorics…