Constrained Optimization on Riemannian Manifolds
Explore advanced mathematical techniques for solving optimization problems on curved spaces, with applications in machine learning and data analysis.
Crash Course in Riemannian Geometry by Harish Seshadri
Introductory lecture on Riemannian geometry, covering fundamental concepts and principles for graduate-level students in mathematics and theoretical physics.
Approximate and Discrete Vector Bundles
Explore synchronization problems and dimensionality reduction through vector bundles. Learn how characteristic classes provide insights into global synchronization and data analysis challenges.
Persistent Stiefel-Whitney Classes
Explore persistent Stiefel-Whitney classes in topological data analysis, extending beyond homology groups to estimate vector bundle structures from finite samples using a persistent approach.
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.
Curvature Bounds and the Length of the Shortest Closed Geodesic
Explore upper bounds for shortest periodic geodesics on Riemannian manifolds, examining curvature's impact on closed geodesic length in various geometric contexts.
Michael Farber - Topological Complexity of Spherical Bundles
Explore parametrized motion planning algorithms and the topological complexity of sphere bundles, examining characteristic classes and specific examples in applied algebraic topology.
Yevgeny Liokumovich - Urysohn Width, Isoperimetric Inequalities and Scalar Curvature
Explore metric spaces, Hausdorff measure, and continuous mappings. Discover connections to isoperimetric inequalities and Riemannian geometry's positive scalar curvature.
An Introduction to Spectral Data for Higgs Bundles
Explore spectral data for Higgs bundles, a key concept in algebraic geometry and mathematical physics, with insights on integrable systems and moduli spaces.
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.
Subtly Knotted Surfaces Separated by Many Internal Stabilizations
Exploration of smoothly knotted surfaces in 4-manifolds, focusing on isotopy, internal stabilizations, and diffeomorphisms. Discusses infinite collections of surfaces with unique properties and infinite stabilization diameter.
Smooth Closing Lemma for Area-Preserving Diffeomorphisms of Surfaces
Explore the smooth closing lemma for area-preserving diffeomorphisms on surfaces, featuring a proof based on Weyl formula and Seiberg-Witten Floer homology. Joint work with Cristofaro-Gardiner and Prasad.
Nearly Parallel G2-Structures on 7-Manifolds - Associative 3-Folds in Aloff-Wallach Spaces
Explore nearly parallel G2-structures on 7-manifolds, focusing on Aloff-Wallach spaces and Sasaki-Einstein manifolds. Learn about associative 3-folds and their construction in these spaces.
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.
Generalized Kaehler and Bihermitian Structures
Explore generalized Kaehler structures, their properties, and similarities to Kaehler case. Covers stability under deformations, Calabi-Yau problem, and period map in complex geometry.
Derived Categories and Motives of Moduli Spaces of Vector Bundles on Curves
Explore derived categories and motives of moduli spaces of vector bundles on curves, their relationships, and recent developments in algebraic geometry.
Stability Structures in Holomorphic Morse-Novikov Theory
Explore complex symplectic manifolds, Floer theory, and Morse-Novikov theory. Delve into analytic questions of convergence and generalization to almost-complex cases in this advanced mathematical lecture.
Basic Remarks on Lagrangian Submanifolds of Hyper-Kähler Manifolds
Explore properties of Lagrangian subvarieties in hyper-Kähler manifolds, focusing on their interaction with Lagrangian fibrations and albanese dimension of Lagrangian surfaces.
On the Deleted Squares of Lens Spaces
Explores homotopy equivalence of configuration spaces in lens spaces, using differential characters and Massey products to investigate topological properties of deleted squares.
Open-Relative Correspondence and Topological Recursion
Explore the connection between open Gromov-Witten invariants and relative Gromov-Witten invariants in symplectic geometry, and their relation to topological recursion.
Quantum Spectrum in Algebraic Geometry I
Explore quantum spectrum in algebraic geometry, focusing on quantum blow-up formula and its applications in birational geometry, motivic measures, and singularity resolution.