Math for Society
Explore misleading graphs, convex regions, compactness, polls, expected value, compound interest, exponential functions, and logarithms to enhance your mathematical understanding for real-world applications.
Floating Bodies and Duality in Spaces of Constant Curvature
Explores p-affine surface area and floating bodies in curved spaces, extending Meyer & Werner's Euclidean results to spherical and hyperbolic geometries. Examines limiting behavior as curvature approaches zero.
Some Problems About Centroids of Convex Bodies
Explore recent advancements in understanding centers of mass for convex bodies, delving into mathematical concepts and their implications.
The Convex Geometry of Blind Deconvolution and Matrix Completion Revisited
Explores convex geometry in blind deconvolution and matrix completion, analyzing dimensional factors in noise bounds and proposing alternative error scaling approaches for low-rank matrix recovery problems.
Daniel Dadush- Integer Programming and the Kannan-Lovasz Conjecture
Explore advanced integer programming techniques, lattice theory, and the Kannan-Lovasz conjecture in this high-level overview of solving n-variable integer programs efficiently, with insights into recent progress and key concepts.
Nonrational Toric Geometry III - Quasifolds, Foliations, Combinatorics and One-parameter Families
Explores nonrational toric geometry through quasifolds, foliations, and combinatorics, extending classical toric geometry to new contexts and examining one-parameter families of toric quasifolds.
On Some Tight Convexity Inequalities for Symmetric Convex Sets
Explores tight convexity inequalities for symmetric convex sets, focusing on Gaussian measure, isoperimetric problems, and Dirichlet-Poincare inequality. Discusses progress using L2 methods and energy minimization.
On Yuansi Chen's Work on the KLS Conjecture I
Explore the KLS conjecture in high-dimensional geometry, its implications for Bourgain's slicing problem, and recent progress using Eldan's Stochastic Localization technique.
Keith Ball- The Probabilistic Character of Convex Domains
Explore the probabilistic nature of convex domains with mathematician Keith Ball, delving into geometric concepts and their applications in probability theory.
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.
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.
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.
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.
Dynamics and Symmetry of Ancient Convex Mean Curvature Flows - Lecture 5
Explore dynamics and symmetry of ancient convex mean curvature flows in this advanced mathematics lecture by Sigurd Angenent from the University of Wisconsin-Madison.
A Generalized Central Limit Conjecture for Convex Bodies
Explore a generalized central limit theorem for convex bodies, its connection to the KLS conjecture, and implications for asymptotic convex geometry in this advanced mathematics lecture.
Local Uniqueness Results for Centroid Bodies
Explore local uniqueness of centroid bodies through hyperplane conditions, examining volume, area, inertia, and distance properties to determine if specific combinations imply a Euclidean ball shape.
Pierre Calka- Close-Up on Random Convex Hulls
Explore random convex hulls, Hausdorff distance, and asymptotic expansions in this mathematical talk on geometric probability and stochastic geometry.
The Aleksandrov Projection Theorem for Convex Lattice Polygons
Explore the discrete analogue of Aleksandrov's projection theorem for convex lattice polygons, examining counterexamples and their implications in Z^2.