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.
On the Gaussian Minkowski Problem
Explore the Minkowski problem for Gaussian surface area measure, examining uniqueness and existence results in this collaborative research presentation.
Concentration Functions and Entropy Bounds for Discrete Log-Concave Distributions
Explore concentration functions and entropy bounds for discrete log-concave distributions, with applications to entropy power inequalities. Based on joint research in probability theory.
Stochastic Analysis and Geometric Functional Inequalities
Explore methods for proving functional inequalities in hypoelliptic diffusions, including geometric and probabilistic approaches, with applications to Langevin dynamics ergodicity.
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.
Peter Pivovarov- Random S-Concave Functions and Isoperimetry
Explore stochastic geometry of s-concave functions, local stochastic isoperimetry, and shadow systems. Discover functional inequalities and their applications in this advanced mathematical discussion.
Schramm-Steif Variance Inequalities for Poisson Processes and Noise Sensitivity
Explore Poisson processes, variance inequalities, and noise sensitivity in stochastic geometry. Gain insights into k-percolation and the Poisson Boolean model with bounded grains.
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.
A Remark on the Minimal Dispersion
Explore improved upper bounds for minimal dispersion in unit cubes, with some results sharp to logarithmic factors. Gain insights into this mathematical concept.
Random Tessellations in Hyperbolic Space - First Steps
Explore random tessellations in hyperbolic space, focusing on Poisson hyperplane tessellations and their unique dimension-dependent phenomena compared to Euclidean and spherical spaces.
An Overview on a Young Research Topic - Valuations on Spaces of Functions
Explore valuations on function spaces, from convex bodies to Lipschitz and convex functions. Learn about recent classifications and advancements in this emerging mathematical field.
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.
Generalized Permutahedra and Optimal Auctions
Explore SIM-bodies as generalized permutahedra, their role in Straight-Jacket Auctions, and the application of computer algebra for determining optimal prices and revenues in auction theory.