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…
What is the cheapest way to superhedge a path-dependent derivative security? If liquid European calls and the underlying risky stock can be used for hedging, then the lowest superhedging price corresponds…
The solution of large sparse linear systems is an essential building block in many science and engineering applications. It is also often the main computational bottleneck. For large problems, direct…
Hyperbolic polynomials are coordinate free generalization to the notion of real rooted polynomials. A special class of hyperbolic polynomials are determinantal polynomials and they bound spectrahedra, feasible sets of semidefinite…
We study the problem of prediction of binary sequences with expert advice in the online setting, which is a classic example of online machine learning. We interpret the binary sequence as the price history of…
Schubert calculus has its origins in enumerative questions asked by the geometers of the 19th century, such as “how many lines meet four fixed lines in three-space?” These problems can…
Many polynomials in combinatorics (and in other areas of mathematics) have nice properties such as having all of their roots being real numbers, or having all of their coefficients being…
In this brief talk, I introduce Archimedean Riesz spaces, also known as vector lattices, and their Archimedean Riesz space tensor product as defined by Fremlin. I define what it means…