Courant, Bezout, and Persistence - Lecture 2
Explore spectral geometry through persistence modules and barcodes, examining oscillation of functions and applications to Courant's nodal domain theorem and Bezout's theorem in eigenfunctions.
Courant, Bezout, and Persistence in Spectral Geometry - Lecture 1
Explore spectral geometry and topological persistence, focusing on oscillation of functions, Courant's nodal domain theorem, and Bezout's theorem in the context of eigenfunctions.
Sharp Concavity of the Isoperimetric Profile Under Lower Ricci Bounds - Workshop on Synthetic Curvature Bounds
Explore sharp concavity of isoperimetric profiles in RCD spaces, extending Bavard-Pansu's work on Ricci curvature bounds to non-smooth, finite-dimensional settings.
Robot Learning From Few Demonstrations by Exploiting Data Structure and Geometry
Explore robot learning from limited demonstrations, leveraging data structure and geometry. Discover optimal control strategies and intuitive interfaces for efficient skill acquisition in human-robot interaction.
Barcodes for the Topological Analysis of Gradient-Like Vector Fields
Explore topological analysis of gradient-like vector fields using barcodes. Learn about chain complexes, parametrization, and applications in smooth and discrete settings, with insights on stability and approximation.
Mikhail Katz - Collapsing Surfaces
Exploring surface collapse in Riemannian geometry, focusing on critical points, intersection theory, and Toponogov comparison. Analyzes fiber homotopy and discrete integration against Euler characteristic.
Geodesic Complexity of Riemannian Manifolds
Explore geodesic complexity in Riemannian manifolds, connecting robot motion planning to topology and geometry. Learn about cut loci, bounds, and applications in this advanced mathematical talk.
Harmonic Maps and Rigidity
Explore harmonic maps, rigidity theorems, and their applications in geometry. Delve into existence theory, Mostow's strong rigidity, and approaches to rigidity using harmonic maps and the Bochner method.
Constrained Optimization on Riemannian Manifolds
Explore advanced mathematical techniques for solving optimization problems on curved spaces, with applications in machine learning and data analysis.
Isoperimetric Inequality for Hausdorff Contents and Its Applications
Explore isoperimetric inequality for Hausdorff contents, its applications in systolic geometry, and new systolic inequalities for non-simply connected Riemannian manifolds.
Towards a Theory of Non-commutative Optimization - Geodesic First and Second Order Methods for Moment Maps and Polytopes
Explore non-commutative optimization theory for geodesically convex problems, unifying diverse applications in computer science, mathematics, and physics through innovative first and second-order methods.
Laurent Saloff-Coste - Breaking Heat Kernel Estimates Into Pieces
Breaking heat kernel estimates on Riemannian manifolds by analyzing pieces separately and reconstructing the whole. Explores Brownian motion within segments and transitions between them.
Metric Reconstruction via Optimal Transport
Explores metric reconstruction using optimal transport theory, introducing Vietoris-Rips thickening to recover metric information from point samples in metric spaces, with applications to Riemannian manifolds.
Exploiting Geometric Structure in Matrix-Valued Optimization
Exploring optimization on matrix manifolds, introducing Riemannian Frank-Wolfe methods for constrained problems, and discussing applications in machine learning and mathematics.
Geodesic Complexity and Fibered Decompositions of Cut Loci
Explore geodesic complexity in Riemannian manifolds, focusing on cut locus structure and fibered decompositions to establish bounds and applications in projective and lens spaces.
Brunn-Minkowski Inequalities for Sprays on Riemannian Surfaces
Generalization of Minkowski average on Riemannian manifolds, characterizing curve families on surfaces satisfying Brunn-Minkowski inequality. Explores conditions for constant-speed curves and geodesic curvature.
Convergence of Manifolds and Metric Spaces
Explore Riemannian manifolds, Gromov-Hausdorff and Intrinsic Flat distances, and their applications in solving stability problems in metric spaces.
Minimal Surfaces in Geometry and General Relativity
Explore the fascinating intersection of minimal surfaces with geometry and general relativity, delving into their mathematical properties and applications in physics.
Nonlinear Hyperbolic Conservation Laws on Manifolds
Explore nonlinear scalar hyperbolic equations on Riemannian varieties, covering existence, uniqueness, entropy conditions, finite-volume schemes, and numerical results.
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.
Quantitative Recurrence for Z-Extension of Three-Dimensional Axiom A Flows
Explore quantitative recurrence in Z-extension of Axiom A flows, focusing on first return time behavior and applications to geodesic flows on Z-cover of compact surfaces.