Members Seminar

From Gromov to the Moon

Joel Fish
Massachusetts Institute of Technology; Member, School of Mathematics
December 2, 2013
I will present some recent applications of symplectic geometry to the restricted three body problem. More specifically, I will discuss how Gromov's original study of pseudoholomorphic curves in the complex projective plane has led to the construction of global surfaces of section, and more generally finite energy foliations, below and slightly above the first Lagrange point in the regularized planar circular restricted three body problem. The talk will be accessible to a general mathematical audience.

Random Cayley Graphs

Noga Alon
Tel Aviv University; Member, School of Mathematics
November 25, 2013
The study of random Cayley graphs of finite groups is related to the investigation of Expanders and to problems in Combinatorial Number Theory and in Information Theory. I will discuss this topic, describing the motivation and focusing on the question of estimating the chromatic number of a random Cayley graph of a given group with a prescribed number of generators.

Interacting Brownian motions in the Kadar-Parisi-Zhang universality class

Herbert Spohn
Technische Universitaet Muenchen; Member, School of Mathematics
November 18, 2013
A widely studied model from statistical physics consists of many (one-dimensional) Brownian motions interacting through a pair potential. The large scale behavior of this model has has been investigated by Varadhan, Yau, and others in the 90's. As a crucial property the model satisfies time-reversibility (alias detailed balance). Once this symmetry is broken, generically one crosses into the KPZ class. Two specific examples will be discussed.

cdh methods in K-theory and Hochschild homology

Charles Weibel
Rutgers University; Member, School of Mathematics
November 11, 2013

This is intended to be a survey talk, accessible to a general mathematical audience. The cdh topology was created by Voevodsky to extend motivic cohomology from smooth varieties to singular varieties, assuming resolution of singularities (for example complex varieties). The slogan is that every variety is locally smooth in this topology. Adapting this to algebraic K-theory has led to several breakthroughs in computation, and clarified connections between the "singular" part of K-theory and Hodge theory.