Course on spin glasses

Date: 
2015/02/24 Tue 10:00 - 12:00
2015/03/11 Wed 10:00 - 12:00
2015/03/19 Thu 15:00 - 17:00
2015/03/23 Mon 15:00 - 17:00
2015/03/25 Wed 13:15 - 15:15
Speaker: 
Erwin Bolthausen
Affiliation: 
Kyoto University and University of Zürich
Abstract: 

Date, time and place: Building No.3
1st: 02/24(Tue) 10:00--12:00 [Room 552]
2nd: 03/11(Wed) 10:00--12:00 [Room 127]
3rd: 03/19(Thu) 15:00--17:00 [Room 127]
4th: 03/23(Mon) 15:00--17:00 [Room 127]
5th: 03/25(Wed) 13:15--15:15 [Room 552][followed by Kansai Seminar]

Lecture notes [final ver.]

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.