High Dimensional Measures - Geometric and Probabilistic Aspects

Attend a comprehensive workshop exploring the geometric and probabilistic aspects of high-dimensional measures through 22 specialized lectures delivered by leading mathematicians. Delve into cutting-edge research topics including functional inequalities on sub-Riemannian manifolds, asymptotic geometry of Schatten class unit balls, and sparse Bernoulli matrix analysis. Examine fundamental problems in convex geometry such as the Gaussian Minkowski problem, Blaschke-Santaló inequalities, and the Mahler conjecture for log-concave functions. Explore advanced topics in geometric probability including the KLS conjecture, random graph matching with noise robustness, and outlier behavior in sparse Wigner matrices. Investigate intrinsic volumes on pseudo-Riemannian manifolds, the Alexandrov-Fenchel inequality, and applications of the Riesz representation theorem to log-concave functions. Learn about equilibrium floating bodies, convexity inequalities for symmetric sets, and isotropy reduction algorithms. Discover recent developments in multivariate statistics through quantiles and depth functions, magnitude theory in L1 subspaces, and non-asymptotic results for Gaussian matrix products, while gaining insights into the fundamental gap of the Dirichlet Laplacian in hyperbolic spaces and solutions to classical Busemann-Petty problems.

Syllabus

Emanuel Milman: Functional Inequalities on sub-Riemannian manifolds via QCD
Olivier Guédon: On the asymptotic geometry of the unit ball of Schatten classes
Han Huang: Rank of Sparse Bernoulli Matrices
Dongmeng Xi: On the Gaussian Minkowski Problem
Franz Schuster: Blaschke–Santaló Inequalities for Minkowski and Asplund Endomorphisms
Andreas Bernig: Intrinsic volumes on pseudo-Riemannian manifolds
Bo’az Klartag: One more proof of the Alexandrov-Fenchel inequality
Yuansi Chen: Recent progress on the KLS conjecture
Stanislaw Szarek: The projective/injective ratio and GPTs
Stanislav Nagy: Quantiles, depth, and symmetries: Geometry in multivariate statistics
M. Fradelizi: The functional form of Mahler conjecture for even log-concave functions in dimension 2
Liran Rotem: Riesz Representation Theorem for Log-Concave Functions
Dmitry Ryabogin: On bodies floating in equilibrium in every direction
Konstantin Tikhomirov: Random Graph Matching with Improved Noise Robustness
Pierre Youssef: Outliers in sparse Wigner matrices
Galyna Livshyts: On some tight convexity inequalities for symmetric convex sets
Santosh Vempala: Reducing Isotropy to KLS: An Almost Cubic Volume Algorithm
Alina Stancu: Some comments on the fundamental gap of the Dirichlet Laplacian in hyperbolic space
Vlad Yaskin: A solution to the 5th and 8th Busemann-Petty problems near the Euclidean ball
Mark Meckes: Magnitude and intrinsic volumes in subspaces of L1
Grigorios Paouris: Non-Asymptotic results for singular values of Gaussian matrix products