Mike Thompson, the Managing Director and CEO of First Analytics, will be giving a seminar on how machine learning and mathematics are used to handle large data analytics programs at First Analytics.
Chaos refers to seemingly random and unpredictable dynamics of a system that evolves in time. Certain chaotic systems exhibit an additional level of complexity: intermittent extreme events that are noticeably distinct from the usual chaotic dynamics. These extreme events include ocean rogue waves, extreme weather patterns, and epileptic seizure. I will discuss several examples of these…
An afternoon workshop/discussion lead by Ilse Ipsen on preparing your research statements and CVs for the job search.
The fundamental basis of the Hopf algebra of quasisymmetric functions, QSym, can be thought of in terms of shuffling permutations. We can think of QSym as having a basis indexed by equivalence classes of permutations, where we identify permutations with the same descent set. This descent set, Des, is a simple example of a permutation…
Self-duality equations in gauge theory can be complexified in many inequivalent ways, but there are two obvious options: One can extend Hodge duality in either a complex linear fashion, or in a conjugate linear one. In general, the two cases result in two very different equations. The first case was first studied by Haydys, while…
Mappings between domains are among the most basic and versatile tools used in the computational analysis and manipulation of shapes. Their applications range from animation in computer graphics to analysis of anatomical variation and anomaly detection in medicine and biology. My talk will start with a brief overview of discrete computational shape mapping, surface parameterization…
Recently, in a series of joint papers with F. Alabau-Boussouira and C. Urbani, I have studied the response of an evolution equation on a Hilbert space to the action of a bilinear control. As is well-known, a bilinear control is a scalar function of time multiplying one of the coefficient of the equation (usually, a…
The study of the structural properties of the set of points at which the viscosity solution of a first order Hamilton–Jacobi equation fails to be differentiable—in short, the singular set—started with the paper On the Singularities of Viscosity Solutions to Hamilton–Jacobi–Bellman Equations, Indiana Univ. Math. J. 36 (1987), 501–524 by Mete Soner and myself. These…
From x-ray machines to luggage scanners, our lives depend on imaging devices that let us “see” what is impossible to observe with the naked eye. I will explain some of the mathematical ideas that make image reconstructions possible. Along the way, we will solve some fun puzzles that are related to image reconstructions. This talk…
The Italian Renaissance painters began to incorporate perspective into their drawings in the 1400’s, but our eyes naturally understand depth from the 2-dimensional image on the back of our eyeball. It’s this projection on the retina that allows mathematicians to represent field of view with the projective plane, and in this talk we’ll investigate what makes it so difficult to…
Independence polynomials are generating functions for the number of independent sets of each cardinality in a graph G. In addition to encoding useful information about the graph (such as the number of vertices, the number of edges and the independence number), the analytic and algebraic properties can say much about the shape and inter-dependence of…
In the first part of the talk we will discuss famous topological and dynamical questions and conjectures about character varieties and the associated action of the mapping class group. In the second part of the talk we will discuss joint work with F. Palesi and T. Yang about type-preserving representations of the fundamental group of the three-holed projective…
Two fluid flow in porous medium systems is an important application in many different areas of science and engineering. Overwhelmingly, it is necessary to mathematically model the behavior of applications of concern at an averaged scale where the juxtaposed position of the phases is not resolved in detail. This length scale is called the macroscale…
We all tackle hard problems everyday, like finding a parking spot in the Dan Allen Deck. However, there are special types of problems which are hard even for a computer to solve. Reductions, conversions of one problem into another, play a critical role in determining the hardness of these computational problems, and lead to philosophical questions…
An afternoon discussion/workshop by Jo-Ann Cohen on preparing teaching and diversity statements for the job search. Note unusual time!
This paper studies the valuation of American options for a general one-factor stochastic volatility model. Using the local time-space calculus on surfaces we derive an early exercise premium representation for the option price, parametrized by the optimal exercise surface. The exercise surface is the unique solution to an integral equation of Volterra type. The paper…