The Foias Lectures
The Foias Lectures honor Distinguished University Professor Ciprian Foias, who has been a member of the Department of Mathematics since 2000. Foias Lecturers are distinguished mathematicians who work in some branch of analysis. They deliver up to three lectures over the course of a week during the academic year. The series is made possible by an endowment established through generous initial gifts by Professors Ron Douglas and Carl Pearcy in 2014, augmented by contributions from friends and colleagues of Professor Foias (matched by a magnanimous anonymous donor). Initial support is also provided by the Powell Chair in Mathematics and the Mobil Chair in Computational Science.

Date Time 
Location  Speaker 
Title – click for abstract 

11/05 4:00pm 
Blocker 117 
Peter Markowich KAUST 
On Wigner and Bohmian Measures in Semiclassical Quantum Mechanics
We present different approaches to the semiclassical limit of the Schrödinger equation,including the (position space based) WKB, the (phase space based) Wigner and the fluidlike Bohmian approach. We point out the interrelations of these approaches, which give a ’transition’ from quantum to classical mechanics, illustrate their strengths and weaknesses and connections to classical fluid/gas dynamics. 

11/06 4:00pm 
Blocker 117 
Peter Markowich KAUST 
Continuum Modeling of Transportation Networks with Differential Equations
We present a discrete ODE and continuum PDE modeling framework for biological transportation networks, which can be used to describe leaf venation, neuronal networks, blood vessel networks etc. The differential equations, which are based on first principles, are capable of modeling network formation, evolution and adaptation. Many mathematical difficulties arise, like instabilities, formation of (thin patterns, multiple steady states, singular scaling limits etc. 

11/07 4:00pm 
Blocker 220 
Peter Markowich KAUST 
Propagation of Monokinetic Phase Space Measures with Rough Momentum Profiles
Consider a Radon measure which is a phase space probability density carried by the graph of a Lipschitz continuous (or even less regular) vector field. We study the structure of the pushforward of such a measure by a Hamiltonian flow. In particular, we provide an estimate on the number of folds in the support of the transported measure. We also study in detail the type of singularities in the projection of the transported measure in configuration space (averaging out the momentum variable). We analyze the conditions under which this projected measure can have atoms, and give an example in which the projected measure is singular with respect to the Lebesgue measure and diffuse. We discuss applications of our results to the classical limit of the Schrödinger equation. Finally we present various examples and counterexamples showing that our results are sharp. 