Introduction to Fukaya Categories - James Pascaleff
Explore Floer cohomology and Fukaya category fundamentals, including Lagrangian intersection theory, Floer differential, A∞ operations, and Gromov compactification in symplectic geometry.
Remarks on Lagrangian Submanifolds of Hyper-Kaehler Manifolds
Explore properties of Lagrangian subvarieties in hyper-Kaehler manifolds, focusing on interactions with Lagrangian fibrations and albanese dimension of Lagrangian surfaces.
Graduate Course on the Tangent Groupoid in Noncommutative Geometry - Lecture 1
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Graduate Course on the Tangent Groupoid in Noncommutative Geometry - Lecture 2
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in mathematical physics and operator algebras.
Classification of Cuntz-Pimsner Algebras Associated to Vector Bundles - Part II
Explore advanced concepts in operator algebras, focusing on the classification of Cuntz-Pimsner algebras associated with vector bundles in this in-depth mathematical seminar.
Classification of Cuntz-Pimsner Algebras Associated to Vector Bundles, Part I
Explore the classification of Cuntz-Pimsner algebras associated with vector bundles in this advanced mathematics seminar by Maria Grazia Viola from Lakehead University.
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.
Superlinear Structures and Conformal Geometry
Explore superlinear structures and conformal geometry, from historical roots to modern applications in physics and mathematics, with insights on representation theory and potential links to the standard model.
Michael Bronstein: Physics-Inspired Graph Neural Networks
Explore physics-inspired continuous learning models for graph neural networks, leveraging tools from differential geometry and algebraic topology to enhance expressive power beyond traditional message-passing paradigms.
Physics-Inspired Learning on Graph - Michael Bronstein, PhD
Explore physics-inspired continuous learning models for graphs, challenging traditional message-passing paradigms. Discover new approaches using differential geometry, algebraic topology, and differential equations to revolutionize graph machine learning.
Equivariant A-Theory & Spaces of Equivariant H-Cobordisms
Explore equivariant A-theory and h-cobordisms, focusing on Waldhausen's algebraic K-theory of manifolds and its role in classifying manifolds and diffeomorphisms.
Why All Maps Are Wrong - Theorema Egregium
Explore Theorema Egregium's geometric proof, revealing why no world map can preserve both area and angles. Understand curvature, spherical areas, and the Gauss map in this mathematical journey.
Quadrature Rules on Manifolds - Useful Results - Lecture 3
Explore advanced quadrature techniques for manifolds, focusing on key results and applications in harmonic analysis. Gain insights into cutting-edge mathematical approaches.
Tangent Groupoid in Noncommutative Geometry - Lecture 12
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
Graduate Course on the Tangent Groupoid in Noncommutative Geometry - Lecture 13
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.
A Geometric Approach to Modeling and Analysis of Mixed-Dimensional and Multi-Continuum Materials
Explore geometric modeling of complex materials, unifying concepts from differential geometry and functional analysis to analyze fractured porous media and multi-continuum models.
Directed Mean Curvature Flow in Noisy Environment
Explore directed mean curvature flow in noisy environments and its connection to the KPZ equation through advanced mathematical analysis and stochastic PDEs.
The Thresholding Scheme for Mean Curvature Flow and De Giorgi's Ideas for Gradient Flows
Explores the thresholding scheme for mean curvature flow in multi-phase systems, its applications in grain growth, and convergence proofs based on De Giorgi's gradient flow ideas.
Generalized Logarithmic Transformation in Exotic Spheres and Homotopy Hopf Manifolds
Explore generalized logarithmic transformations in topology, including $\star$-diagrams, spherical T-duality, and applications to exotic spheres and homotopy Hopf manifolds.
Spherical T-Duality Meets Exotic Spheres and Homotopy Hopf Manifolds
Explore spherical T-duality, its relation to 7-dimensional homotopy spheres, and implications for complex structures on exotic manifolds in this advanced mathematical discussion.
Tangent Groupoid in Noncommutative Geometry - Lecture 5
Explore advanced concepts in noncommutative geometry, focusing on the tangent groupoid and its applications in graduate-level mathematics.