Explore advanced mathematical techniques at the intersection of calculus of variations, probability theory, and geometry through this comprehensive workshop from the Institute for Pure & Applied Mathematics. Delve into cutting-edge research on isoperimetric-type inequalities in Euclidean space and their applications in geometric probability theory, examining how symmetry and structure influence various families of mathematical inequalities. Investigate the connections between differential geometry concepts like mean curvature flow and isoperimetric problems with respect to Gaussian measures, building on foundational work including Huisken's monotonicity formula. Discover applications spanning theoretical computer science and social choice theory, including computational hardness problems for MAX-CUT and the Majority is Stablest Theorem. Learn about recent breakthrough developments on the KLS-conjecture and its implications for arbitrary Euclidean convex sets. Engage with presentations from leading researchers covering topics such as high-dimensional L_p-balls, the Reverse Brascamp Lieb Inequality, fundamental gap estimates for convex domains, empirical isoperimetric inequalities, spectral inequalities for rotation invariant measures, quantitative stability in geometric and functional inequalities, the log-Minkowski Problem, eigenvalue estimates for p-Laplace problems, Brownian transport maps, entropy and stability of hypersurfaces, volume of p-zonoids, Gibbs sampling for convex bodies, large deviations principles, and variational proofs of isoperimetric inequalities.

Syllabus

Bo'az Klartag - Size of line intersections in high dimensional L_p-balls and product measures
Karoly Boroczky - Equality in the Reverse Brascamp Lieb Inequality - IPAM at UCLA
Guofang Wei - Fundamental Gap Estimate for Convex Domains - IPAM at UCLA
Grigorios Paouris - Empirical Isoperimetric Inequalities outside convexity - IPAM at UCLA
Orli Herscovici - Kohler-Jobin Meets Ehrhard - IPAM at UCLA
Liran Rotem - Spectral inequalities for rotation invariant measures - IPAM at UCLA
Shay Shadovsky - Involutions and costs: A zoo of dualities - IPAM at UCLA
Alessio Figalli - Quantitative Stability in Geometric and Functional Inequalities - IPAM at UCLA
Galyna Livshyts - On a conjectural symmetric version of the Ehrhard inequality
Dima Ryabogin - On Ulam's Problem 19 and related problems - IPAM at UCLA
Tobias Colding - Singularities and diffeomorphism - IPAM at UCLA
Emanuel Milman - The log-Minkowski Problem - IPAM at UCLA
Barbara Brandolini - Eigenvalue estimates for p-Laplace problems & domains in Fermi Coordinates
Han Huang - When can we recover an Erdos-Renyi graph from its local structure? - IPAM at UCLA
Lu Wang - Topological properties of hypersurfaces with low entropy - IPAM at UCLA
Yair Shenfeld - The Brownian transport map - IPAM at UCLA
Jacob Bernstein - Entropy and C^0 stability of hypersurfaces - IPAM at UCLA
Eugenia Saorin-Gomez - Inner parallel bodies & the Isoperimetric Quotient
Matthieu Fradelizi - Volume of p-zonoids and inequalities for determinants
Santosh Vempala - Gibbs Sampling for Convex Bodies and an L_0 Isoperimetric Inequality
Joe Neeman - Large deviations for triangle densities
Jonathan J. Zhu - Waists, widths and symplectic embeddings
Francesco Chiacchio - A class of isoperimetric problems with double density and applications
Maria Gordina - Large deviations principle for sub-Riemannian random walks on Carnot groups
Assaf Naor - Extension, separation and isomorphic reverse isoperimetry
Steven Heilman - Variational Proofs of Isoperimetric Inequalities