Symmetries of Manifolds - Lecture 3
Explore symmetries of manifolds in topology and geometry. Delve into classical and recent results, methods, and emerging conjectures about symmetry spaces of simple manifolds like spheres and discs.
Symmetries of Manifolds - Lecture 2
Delve into symmetries of manifolds, exploring classical and recent results on spaces of symmetries for simple manifolds like spheres and discs, with insights into emerging conjectural perspectives.
Symmetries of Manifolds - Lecture 1
Explore symmetries of manifolds in topology and geometry. Delve into classical and recent results, methods, and emerging conjectures about symmetry spaces of simple manifolds like spheres and discs.
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.
An Intrinsic Persistent Homology Transform
Explores an intrinsic persistent homology transform for metric spaces, focusing on metric graphs. Discusses injectivity results and compares to related constructs in topological data analysis.
Entropy and C^0 Stability of Hypersurfaces - IPAM at UCLA
Explore entropy's role in hypersurface complexity, focusing on sphere rigidity, stability properties, and generalizations in higher dimensions. Gain insights into cutting-edge research in geometric analysis.
Convex Sunflower Theorems and Neural Codes
Explore convex sunflower theorems and neural codes, connecting neuroscience with discrete geometry to understand place cell encoding and cognitive mapping in rat hippocampus.
Borsuk-Ulam Theorems into Higher-Dimensional Codomains
Exploration of Borsuk-Ulam theorems in higher dimensions, generalizing results and discussing open questions related to optimal diameters and Schur polynomials.
Johnathan Bush - Maps of Čech and Vietoris–Rips Complexes into Euclidean Spaces
Explore simplex-preserving maps in Čech and Vietoris–Rips complexes, their applications, and the challenge of finding such maps from various domains to Euclidean spaces.
Vanessa Robins - The Extended Persistent Homology Transform for Manifolds with Boundary
Explore extended persistent homology transform for shape analysis, offering finite distances between shapes with different Betti numbers and applications in shape clustering.
Coassociative Fibrations in G2 Geometry
Explore G2 geometry in 7D spaces, focusing on coassociative submanifolds. Learn about their properties, deformation theory, and constructions forming fibrations with singular fibers in 7-manifolds.
Some Comments on the Fundamental Gap of the Dirichlet Laplacian in Hyperbolic Space
Explore the fundamental gap of convex domains in hyperbolic space, comparing it with Euclidean space and examining different types of convexity in this advanced mathematical analysis.
A Survey of Volume Inequalities - Basic Notions Seminar - 2019
Explores volume inequalities in Euclidean space, discussing identities and inequalities for convex sets and star-bodies. Covers Gromov's conjecture and is accessible to a general mathematical audience.
Reconstructing Hidden Geometric Structures in Data From Distance Matrices
Explore techniques for reconstructing metric spaces and embeddings from distance matrices, covering theoretical foundations, practical applications, and open problems in geometric data analysis.
Localization Schemes
Explore innovative localization schemes for analyzing Markov chain mixing times in continuous and discrete spaces, with applications to Ising models and Glauber dynamics.
Differential Operators and the Geometry of Domains in Euclidean Space
Explore the interplay between differential operators and domain geometry in Euclidean space with Tatiana Toro's insightful lecture, the inaugural AMS Maryam Mirzakhani Lecture at JMM 2020.
Homeomorphisms of Euclidean Space
Explore recent advances in understanding the topological group of homeomorphisms of Euclidean space, including methods and emerging conjectures in geometric topology.
General Linear Transformations on Vector Spaces
Explore general linear transformations on vector spaces, their properties, and examples. Learn to distinguish between linear and non-linear transformations in this comprehensive overview.
Looking for p-Energy Forms in Cheeger Spaces
Explore p-energy forms in Cheeger spaces without relying on gradients. Learn about constructing these forms using characteristic features of Cheeger metric measure spaces.
Schoen's Conjecture for Limits of Isoperimetric Surfaces
Explore Schoen's conjecture for asymptotically flat Riemannian manifolds, focusing on area-minimizing hypersurfaces and recent developments in mathematical relativity.
De Rham Algebras of Closed Quasiregularly Elliptic Manifolds are Euclidean
Explore quasiregular mappings and de Rham cohomology in closed manifolds, leading to a homeomorphic classification of certain 4-manifolds.