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UCLA Science Faculty Research Colloquium
Stochastic Models for Large Interacting Systems in the Sciences |
Thomas M. Liggett, Department of Mathematics, UCLA
Monday, January 11, 2010
4:00-5:00pm
Physics & Astronomy Building (PAB), Room 1425
Reception to follow in PAB lobby
Divisions of Life and Physical Sciences, UCLA College of Letters and Science
A forty year old branch of probability theory is devoted to the analysis of large systems in which individuals evolve in time according to rules that include both randomness and interactions. Here is a sampling of these systems, together with some areas that partially motivated them: Voter models (population genetics; tumor growth), Glauber dynamics (Ising model for magnetism; Gibbs samplers), contact processes (spread of infection; Reggeon field theory), and exclusion processes (messenger RNA; traffic flow). The main issues that are dealt with involve the long time behavior of the system, and how it is affected by the details of the evolution rules. In my lecture, I will describe some of these models, and discuss some of the results that have been proved about them.
The UCLA Science Faculty Research Colloquium Series is designed to promote interdisciplinary collaborative research, highlight the research of exceptionally distinguished faculty, and enhance education about significant new research in the sciences. The lectures are designed to be of interest to a general audience.
Poster: View
Video lecture available as a podcast on UCLA on iTunes U. |
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Distinguished Lecture Series: Special Public Lecture
On Mean Field Games |
Pierre-Louis Lions, Collège de France and Ecole Polytechnique
Tuesday, January 5, 2010
4:30-5:30pm
Moore Hall, Room 100
Reception to follow at IPAM (Portola Plaza Bldg)
Institute for Pure and Applied Mathematics (IPAM) and Department of Mathematics
This talk will be a general presentation of Mean Field Games (MFG in short), a new class of mathematical models and problems introduced and studied in collaboration with Jean-Michel Lasry. Roughly speaking, MFG are mathematical models that aim to describe the behavior of a very large number of “agents” who optimize their decisions while taking into account and interacting with the other agents. The derivation of MFG, which can be justified rigorously from Nash equilibria for N players games, letting N go to infinity, leads to new nonlinear systems involving ordinary differential equations or partial differential equations. Many classical systems are particular cases of MFG like, for example, compressible Euler equations, Hartree equations, porous media equations, semilinear elliptic equations, Hamilton-Jacobi-Bellman equations, Vlasov-Boltzmann models ... In this talk we shall explain in a very simple example how MFG models are derived and present some overview of the theory, its connections with many other fields and its applications.
This lecture is part of the Department of Mathematics’ Distinguished Lecture Series and the IPAM workshop “New Directions in Financial Mathematics.” Pierre-Louis Lions is a French mathematician who was awarded the Fields Medal in 1994 for his work on partial differential equations. Lions earned a doctorate from the University of Paris VI in 1979. He is a member of the French Academy of Sciences and Professor at the College de France. For his outstanding contributions to mathematics and its applications, he has received many prestigious awards, including the Doistau-Blutet Foundation Prize, the Ampère Prize, the IBM Prize and the Philip Morris Prize.
Poster: View |
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Public Lecture
The Combinatorics of Voting Paradoxes |
Noga Alon, Professor of Mathematics and Computer Science, Tel Aviv University, Microsoft Research, Israel
Monday, October 5, 2009
4:30-5:30pm
Franz Hall, Room 1178
Reception to follow at IPAM
IPAM, Department of Mathematics and the Computer Science Department
For more information about the lecture, click here.
To view the lecture online, click here. |
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2009 UCLA Day
Department of Mathematics and IPAM Alumni Open House and Reception |
Open house and reception for math alumni and their families, as well as all alumni interested in the power of math to solve many of the world’s problems. Come and network with your fellow alumni and interact with researchers from both the department and the institute, who will present posters on some of their most cutting-edge work.
Saturday, May 9, 2009
5:30-6:30pm
IPAM, Portola Plaza Building
The Department of Mathematics and IPAM
For all-inclusive $20 ticket (parking, tote bag, lunch, barbecue, lectures and tours), click here. |
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Public Symposium
The Convergence of Logic, Mathematics and Computer Science |
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Martin Davis, New York University
Hilbert’s Tenth Problem
I will discuss various aspects of the work that led to a proof that Hilbert\'s Tenth Problem (Diophantine Equations) is unsolvable. The unsolvability result is a consequence of the equivalence between two notions, one from logic/computability theory, the other, from number theory. Interesting and curious applications of this equivalence will be discussed including a universal polynomial equation, a prime representing function, and Diophantine form of famous problems.
Michael O. Rabin, Harvard University and Google Research
Novel Concepts of Proof and Their Applications
Over the past 30 years computer scientists have created new revolutionary notions of mathematical proofs. The introduction of randomness created proofs that allow for a probability of error. Zero Knowledge Proofs (ZKPs) enable a demonstration of a mathematical truth without revealing any information beyond the claimed truth. I will discuss these concepts, present a new practically efficient method for ZKPs, and describe applications to business transactions such as the secure and secrecy preserving conduct of auctions. The talk will be self contained and readily accessible.
Moshe Y. Vardi, Rice University
From Aristotle to the Pentium
Logic started as a branch of philosophy, going back to Greeks in the classical period. Computers are relatively young, dating back to the middle of the 20th century. This talk tells the story of logic begat computers, tracing the path from Aristotle to the Pentium. This is a story full of both intellectual drama, as well as real-life drama, with most of the characters dying young, miserably, or both.
Thursday, April 30, 2009
2:00-7:00pm
Reception to follow at 6:00pm
Kerckhoff Hall, Charles E. Young Grand Salon
The UCLA Logic Center and the Department of Mathematics
Video lectures available through UCLA on iTunes U
Schedule
Abstracts and Bios |
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