Mathematical Physics Seminar

MATHEMATICAL PHYSICS SEMINAR

SPRING 2010 Lectures

Regular meeting time: Tuesdays 4:30--5:30
Place: Jadwin 343

Date	Speaker	Title
Feb. 9	Alain-Sol Sznitman, ETH, Zurich	Disconnection and Random Interlacements The general theme of the talk pertains to the question of understanding how paths of random walks can create large separating interfaces. This question has in particular been investigated in the context of random walk on a discrete cylinder with a large connected base, and when discussing the presence or absence of a giant component in the complement of the trajectory of a random walk on a large discrete torus. We will present an overview of some of the results, and paradigms, which have now emerged and explain how the above problems are related to questions of ercolation and to the model of random interlacements.
Please note special date, time, and location Feb. 19 4:00 IAS S-101	Sourav Chatterjee, UC Berkeley and Courant Institute	Superconcentration We introduce the term `superconcentration' to describe the phenomenon when a function of a Gaussian random field exhibits a far stronger concentration than predicted by classical concentration of measure. We show that when superconcentration happens, the field becomes chaotic under small perturbations and a `multiple valley picture' emerges. Conversely, chaos implies superconcentration. While a few notable examples of superconcentrated functions already exist, e.g. the largest eigenvalue of a GUE matrix, we show that the phenomenon is widespread in physical models; for example, superconcentration is present in the Sherrington-Kirkpatrick model of spin glasses, directed polymers in random environment, the Gaussian free field and the Kauffman-Levin model of evolutionary biology. As a consequence we resolve the long-standing physics conjectures of disorder-chaos and multiple valleys in the Sherrington-Kirkpatrick model, which is one of the focal points of this talk.
Mar. 2	Igor Rodnianski, Princeton University	On the Boltzmann limit of a homogeneous Fermi gas We study the dynamics of the thermal momentum distribution function for an interacting, homogenous Fermi gas on $\Z3$ in the presence of an external weak static random potential, where the pair interactions between the fermions are modeled in dynamical Hartree-Fock theory. We determine the Boltzmann limits associated to different scaling regimes defined by the size of the random potential, and the strength of the fermion interactions.
Mar. 30	Sergiu Klainerman, Princeton University	On the formation of black holes I will discuss some recent results obtained in collaboration with I. Rodnianski on the dynamic formation of black holes for the Vacuum Einstein equations. These results simplify and extend considerably the recent well known result of D. Christodoulou.
Apr. 27	Matthew Hastings, Microsoft Research	Quasi-adiabatic continuation and the Topology of Many-body Quantum Systems Topological arguments play a key role in understanding quantum systems. For example, recently it has been shown that K-theory provides a tool for classifying different phases of non-interacting, or single-particle, systems. However, topological arguments have also been applied to interacting systems. I will explain the technique of quasi-adiabatic continuation, which provides a way to rigourously formulate many of the topological arguments made by physicists for these systems. In particular, I will discuss its application to a higher dimensional Lieb-Schultz-Mattis theorem (a statement about degeneracy of ground states, which can arise for topological reasons), where this technique was introduced in 2004, and its more recent application to proving quantum Hall conductance quantization for interacting systems.