2024 Hayden-Howard Lecture

Felix Otto, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

A Variational Regularity Theory for Optimal Transportation and Its Applications to Matching

Optimal transportation, which identifies an optimal coupling between two probability measures, is a simple to state variational problem with surprisingly diverse connections.  A couple of years ago, with M. Goldman, we devised a new approach to the regularity theory for the coupling. It mimics De Giorgi's approach to the regularity theory of minimal surfaces in the sense that a harmonic approximation result is at its center: Under a non-dimensional smallness condition, the displacement is close to the gradient of a harmonic function. The main advantage of this variational regularity theory over the one based on maximum principle for the Monge-Ampere equation is that it does not require any regularity of the involved measures. Hence it can be applied to the popular matching problem, where it provides regularity on large scales.

About the Speaker:

Felix Otto has been the director at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany, since 2010. His main expertise lies in the applied analysis of partial differential equations and in the calculus of variations, with a recent focus on randomness. He is well known for his work on gradient flow structures of dissipative evolution equations, pattern formation in ferromagnets, and stochastic homogenization. His scientific honors include the A.P. Sloan Research Fellowship, the Max Planck Research Prize, the Leibniz Prize from the German Science Foundation. He was an invited speaker at the 2002 International Congress of Mathematicians in Beijing, China.

Algebraic Topology: There are several different notions of what it might mean for a space to be "even" in algebraic topology, all of which have useful, increasingly algebraic proerties. Mike Hll will begin by describing some classical work due to Wilson, focusing on what sorts of things happen when we have only even cells or homotopy groups, and then he will describe more recent work (all joint with Hopkins), where building on geometric intuition, we construct a version of this that works also when there is an action of a finite group. 

Title: Emergent and Re-emerging diseases: The case of Ebola, Influenza and Tuberculosis

Abstract: As we[1] noted recently, It is about two years since the official confirmation of an outbreak of Ebola haemorrhagic fever in West Africa. With new cases occurring at their lowest rate for 2015 with the end of the outbreak soon after in all three countries predominantly affected. The time to consider systematic approaches strategies to mitigate the impact of future outbreaks of re-emergent diseases like Ebola or Tuberculosis or Influenza; the result of changing complex social landscapes, is overdue. The recent Ebola outbreak, like many other emerging or re-emergent diseases, illustrates the crucial role of the ecological, social, political, and economic context within which diseases emerge[2]. In this lecture, I will explore what we have learned from dealing with emergent and re-emergent diseases including Tuberculosis in the past and in the era of HIV and the what we have learned from the recent out breaks of Influenza and Ebola.

Title:  Singularities in algebraic geometry: how many times does a polynomial vanish at a point?

Abstract:  We all learn early on how to count the number of times a given number appears as a root of a polynomial in one variable. But for polynomials in several variables, the analogous question is much more interesting. The most naive generalization leads to the multiplicity of a singular point on an algebraic curve or hypersurface, and I will review this beautiful chapter of classical algebraic geometry. In recent years a more subtle invariant, defined via considerations of integrability, has come into prominence. I will conclude by discussing how this new invariant governs many analytic, arithmetic and geometric properties of a polynomial.

The 2014 Hayden-Howard Lecture will take place on April 11, 2014 at 4pm in CB 349.  The speaker will be Jill Pipher of Brown University.  The title of her talk will be Geometric Discrepancy Theory. Complete information is available at http://www.math.uky.edu/hayden-howard