Distinguished Lecture Series
Every year, the Distinguished Lecture Series (DLS) brings two to four eminent mathematicians to UCLA for a week or more to give a lecture series on their field, and to meet with faculty and graduate students.
The first lecture of each series is aimed at a general mathematical audience, and offers a rare opportunity to see the state of an area of mathematics from the perspective of one of its leaders. The remaining lectures in the series are usually more advanced, concerning recent developments in the area.
Previous speakers of the DLS include: Peter Sarnak, Peter Schneider, Zhengan Weng, Etienne Ghys, Goro Shimura, Jean Bellissard, Andrei Suslin, Pierre Deligne, Michael Harris, Alexander Lubotzky, Shing-Tau Yau, Hillel Furstenberg, Robert R. Langlands, Clifford Taubes, Louis Nirenberg, Oded Schramm, Louis Nirenberg, I.M. Singer, Jesper Lutzen, L.H. Eliasson, Raoul Bott, Dennis Gaitsgory, Gilles Pisier, Gregg Zuckerman, Freydoon Shahidi, Alain Connes, Jöran Friberg, David Mumford, Sir Michael Atiyah, Jean-Michel Bismut, Jean-Pierre Serre, G. Tian, N. Sibony, C. Deninger, Peter Lax, and Nikolai Reshetikhin.
The DLS is currently supported by the Larry M. Wiener fund.
University of StrasbourgVisit: 04/03/2013 to 04/20/2013
Rheinische Friedrich-Wilhelms-Universität BonnVisit: 05/07/2013 to 05/09/2013
Eötvös Loránd UniversityVisit: 05/28/2013 to 05/30/2013
Texas A&MVisit: 10/22/2013 to 10/26/2013
IAS, PrincetonVisit: 10/30/2013 to 11/06/2013
Duke University / UC BerkeleyVisit: 05/19/2014 to 05/23/2014
October 7th - 3pm
Lecture 1: On Wigner and Bohmian Measures in Semiclassical Quantum Mechanics
Abstract: We present quantum mechanics in three different formulations: the classical Schroedinger picture, the kinetic phase-space Wigner picture and the somewhat less known `quantum-trajectory-type’ Bohmian picture. In particular we discuss the semiclassical limit problem, which is treated by well-known WKB (high) frequency asymptotics in the Schrödinger picture and by kinetic scaling limits in the Wigner picture. Somewhat surprising results come up in the semiclassical limit of the Bohmian formulation, mainly concerning the limits of the Bohmian quantum trajectories. The main mathematical tools are pseudo-differential operators, micro-local analysis and the theories of monokinetic, multikinetic and Young measures.
Main reference: Alessio Figalli, Christian Klein, Peter Markowich and Christof Sparber: WKB analysis of Bohmian dynamics. Comm. Pure Applied Math., 67(4): 581--620, 2014
October 8th - 3pm
Lecture 2: Mathematical Analysis of a PDE System for Biological Network Formation
Abstract: We study an elliptic-parabolic system of partial differential equations recently proposed by D. Hu and D. Cai, which is capable of modeling biological network formation. The model
describes the pressure field obtained from a Darcy type equation and the dynamics of the network conductance under pressure force effects with diffusion representing randomness in the material structure. We prove the existence of global weak solutions and of local mild solutions and study their long term behavior. By energy dissipation we argue that steady states play a central role to understand the pattern capacity of the system. We show that for large diffusion coefficient the trivial steady state is stable. Patterns occur for small diffusion because the zero steady state is Turing unstable in this range; for zero diffusion we exhibit a large class of dynamically stable steady states.
Main reference: Jan Haskovev, Peter Markowich and Benoit Perthame: Mathematical Analysis of a PDE System for Biological Network Formation, to appear in Comm. PDE, 2014
October 9th - 4:30 pm
Lecture 3: Price Formation: from Boltzmann to Free Boundaries
Abstract: We present and analyse a parabolic free boundary (FB) model for the evolution of the price of a good in an economic market with many agents. The model was originally formulated by J.-M.-Lasry and P.-L. Lions in the context of their theory on mean field games. Our analysis of the FB model is based on a simple and surprising geometric method, which relies on a reduction to the one-dimensional heat equation and does not require any of the typical free-boundary regularity techniques. Motivated by the quest of a more explicit derivation of the model we present a mesoscopic Boltzmann-type problem (featuring smooth solutions) and derive the Lasry-Lions Model by a scaling limit (large number of transactions) from it.
Main reference: Martin Burger, Luis Caffarelli, Peter Markowich, Marie-Therese Wolfram: On a Boltzmann-Type Price Formation Model, Proc. Royal Soc. A 469 (2013), 2157 20130126.
About Peter Markowich:
About Yuval Peres:
Yuval Peres (born 1963) is a Principal Researcher in the Theory Group at Microsoft Research in Redmond, WA. He is known for his research in probability theory, ergodic theory, mathematical analysis, theoretical computer science, and in particular for topics such as fractals and Hausdorff measure, random walks, Brownian motion, percolation and Markov chain mixing times. He was born in Israel and obtained his Ph.D. at the Hebrew University of Jerusalem in 1990 under the supervision of Hillel Furstenberg. He was a faculty member at the Hebrew University and the University of California at Berkeley.
Peres was awarded the Rollo Davidson Prize in 1995 and the Loève Prize in 2001. He was an invited speaker at the International Congress of Mathematicians in 2002. In 2011, he was a co-recipient of the David P. Robbins Prize. In 2012 he became a fellow of the American Mathematical Society.
Peres is known as a prolific coauthor of research books and papers. Some of his long-term research collaborators are Itai Benjamini, Amir Dembo, Russell Lyons, Assaf Naor, Robin Pemantle, Oded Schramm, Scott Sheffield, Boris Solomyak and Ofer Zeitouni. He has advised 21 Ph.D students.