Prof. Erwin Bolthausen SGU Special Lecture

SGU Special lectures by Prof. Erwin Bolthausen will take place as follows:

Title
Course on spin glasses
Date / Venue (Faculty of Science Bldg. #3, Kyoto University)
10:00-12:00 Tue, February 24, 2015 [Rm 552]
10:00-12:00 Wed, March 11, 2015 [Rm 127]
15:00-17:00 Thu, March 19, 2015 [Rm 127]
15:00-17:00 Mon, March 23, 2015 [Rm 127]
13:15-15:15 Wed, March 25, 2015 [Rm 552]
Abstract
Lecture 1: Examples of spin glasses: The Sherrington-Kirkpatrick model and the perceptron. Examples from combinatorial optimization. Analysis of the simplest spin glass, the Random Energy Model (REM for short). The Poisson-Dirichlet point process as the limiting object of the REM.

Lecture 2: The Generalized Random Energy Model (GREM). Its limiting object, the Ruelle probability cascades. Time reversal of the Ruelle cascades, the BS-coalescent. The basic invariance properties of the Ruelle cascades and the BS-coalescent.

Lecture 3: Latakos' proof of the replica symmetric solution of the SK-model. Guerra's replica symmetry breaking bound for SK.

Lecture 4: Ultrametricity. Analysis of a simple case, a non-hierarchical version of the GREM. Panchenko's proof of ultrametricity for the SK and other models, based on the Ghirlanda-Guerra identities. His proof of the Parisi formula.

Lecture 5: Either further details of Panchenko's approach, or a discussion of the Thouless-Anderson-Palmer equations (TAP for short) in connection with the cavity approach.

Sponsor
Department of Mathematics, Kyoto University
Research Institute for Mathematical Sciences