Explore the fascinating intersection of high-dimensional geometry and probability theory through this comprehensive winter school featuring leading experts in the field. Delve into advanced topics including variational techniques in stochastic geometry with Giovanni Peccati, who demonstrates how calculus of variations applies to geometric probability problems. Master Gaussian isoperimetry and related concepts through Joe Neeman's systematic treatment of geometric inequalities in high-dimensional spaces. Understand functional inequalities and concentration of measure phenomena with Radek Adamczak's detailed exploration of how probability concentrates in high dimensions. Examine Bo'az Klartag's in-depth analysis of Yuansi Chen's groundbreaking work on the KLS (Kannan-Lovász-Simonovits) conjecture, one of the most important open problems in convex geometry. Learn about geometric probabilities and valuation theory from Monika Ludwig, connecting classical geometric measure theory with modern probabilistic methods. Discover Khinchin inequalities with sharp constants through Tomasz Tkocz's rigorous mathematical treatment. Conclude with Persi Diaconis's tribute lecture on Haar-distributed random matrices, honoring the memory of Elizabeth Meckes while exploring random matrix theory applications. Each topic builds upon fundamental concepts while advancing to cutting-edge research, making complex mathematical relationships accessible through expert instruction and comprehensive coverage of both theoretical foundations and practical applications.

Syllabus

Giovanni Peccati: Some applications of variational techniques in stochastic geometry I
Joe Neeman: Gaussian isoperimetry and related topics I
Radek Adamczak: Functional inequalities and concentration of measure I
Bo’az Klartag: On Yuansi Chen’s work on the KLS conjecture I
Giovanni Peccati: Some applications of variational techniques in stochastic geometry II
Monika Ludwig: Geometric probabilities and valuation theory
Bo’az Klartag: On Yuansi Chen’s work on the KLS conjecture II
Joe Neeman: Gaussian isoperimetry and related topics II
Tomasz Tkocz: Khinchin inequalities with sharp constants
Bo’az Klartag: On Yuansi Chen’s work on the KLS conjecture III
Radek Adamczak: Functional inequalities and concentration of measure II
Giovanni Peccati: Some applications of variational techniques in stochastic geometry III
Joe Neeman: Gaussian isoperimetry and related topics III
Radek Adamczak: Functional inequalities and concentration of measure III
Persi Diaconis: Haar-distributed random matrices - in memory of Elizabeth Meckes