Erwin Bolthausen教授（Kyoto / UZH）による京都大学SGU特別講義を下記の要領で行います。

タイトル

Course on spin glasses

日時・場所

京都大学 理学部３号館
平成２７年２月２４日（火）10：00～12：00　[552講義室]
平成２７年３月１１日（水）10：00～12：00　[127大会議室]
平成２７年３月１９日（木）15：00～17：00　[127大会議室]
平成２７年３月２３日（月）15：00～17：00　[127大会議室]
平成２７年３月２５日（水）13：15～15：15　[552講義室]

概要

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.

主催

京都大学大学院理学研究科数学・数理解析専攻、京都大学数理解析研究所