One More Proof of the Alexandrov-Fenchel Inequality
Explore a concise proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies, presented by Bo'az Klartag in collaboration with other mathematicians.
Intrinsic Volumes on Pseudo-Riemannian Manifolds
Explore intrinsic volumes in pseudo-Riemannian geometry, covering Hadwiger's theorem, Weyl's principle, and Crofton formulas. Learn about recent developments in this advanced mathematical field.
Blaschke–Santaló Inequalities for Minkowski and Asplund Endomorphisms
Explores new isoperimetric inequalities for monotone Minkowski endomorphisms, extending to Asplund endomorphisms of log-concave functions, generalizing the Blaschke–Santaló inequality in convex geometric analysis.
Ilya Molchanov - Random Sets Generated by Translates of a Convex Body
Explores K-hulls and K-strongly convex sets, analyzing facial structures and applying theory to random point samples. Discusses convergence of f-vectors and related probabilistic results.
Facets of High Dimensional Random Polytopes
Explore asymptotic behavior of high-dimensional random polytopes, analyzing facets and their geometric properties as dimensions and data points increase, revealing insights into spherical approximations and tessellations.
The Large Deviations Approach to High-Dimensional Convex Bodies - Lecture I
Explores large deviation principles in high-dimensional convex bodies, focusing on non-universal behaviors in random projections and their relation to underlying geometry.
The Mysterious Extremals of the Alexandrov-Fenchel Inequality
Explore the Alexandrov-Fenchel inequality's extremal bodies, recent progress in characterizing them for convex polytopes, and insights into this fundamental problem in convex geometry.
Functional Inequalities and Concentration of Measure III
Explores concentration inequalities in probability and geometric analysis, focusing on functional inequalities like Poincaré and log-Sobolev. Covers properties, applications to Lipschitz functions, and various measure settings.
Gaussian Isoperimetry and Related Topics III
Explore Gaussian isoperimetry's applications in probability and analysis, including concentration inequalities, noise stability, and Sobolev-type inequalities. Learn proof methods from geometric measure theory.
Functional Inequalities and Concentration of Measure II
Explores concentration inequalities in probability and geometric analysis, focusing on functional inequalities like Poincaré and log-Sobolev. Covers properties, applications to Lipschitz functions, and various measure settings.
Gaussian Isoperimetry and Related Topics II
Explore Gaussian isoperimetry's applications in probability and analysis, including concentration inequalities, noise stability, and Sobolev-type inequalities. Learn proof methods from geometric measure theory.
On Yuansi Chen's Work on the KLS Conjecture II
Explores recent progress on the KLS conjecture in high-dimensional geometry, focusing on Yuansi Chen's work and Eldan's Stochastic Localization technique. Discusses implications for Bourgain's slicing problem.
Separation Theorems in Signed Tropical Convexities
Explores separation theorems in signed tropical convexities, comparing TO and TC-convexities. Presents new results on hyperplane separation, characterizes segments and hemi-spaces, and proves equivalence for generic point collections.
Polyhedral Geometry of Pivot Rules
Explore the geometric perspective on pivot rules in linear programming, connecting polyhedra, simplex methods, and arborescences to gain insights into optimization algorithms.
Regularity of Free Boundaries in Obstacle Problems - Lecture IV
Explore advanced concepts in free boundary problems, focusing on regularity in obstacle problems. Learn key results, current research, and open challenges in this mathematical field.
Regularity of Free Boundaries in Obstacle Problems - Lecture II
Explore free boundary problems in PDE, focusing on regularity in obstacle problems. Learn key results, current research, and open questions in this mathematical field.
The Restriction Problem and the Polynomial Method - Lecture IV
Explore Stein's restriction conjecture, Kakeya conjecture, and the polynomial method in restriction theory. Understand wave packet decomposition and intersection of tubes in hypersurfaces.
The Restriction Problem and the Polynomial Method - Lecture III
Explore Stein's restriction conjecture, Kakeya conjecture, and the polynomial method in restriction theory. Understand wave packet decomposition and intersection of tubes in hypersurfaces.
Differential Geometry - Lecture 14
Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in modern geometry.
Differential Geometry - Lecture 12
Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in modern geometry and physics.
Differential Geometry - Lecture 11
Explore advanced concepts in differential geometry, focusing on complex mathematical theories and their applications in this comprehensive lecture.