Derived Skein Modules via Factorization Homology
Explore derived skein modules through factorization homology, delving into categorical symmetries in quantum field theory.
Lifting Hamiltonian Torus Actions to Integrable Systems
Explore finite dimensional integrability in mathematical physics, focusing on lifting Hamiltonian torus actions to integrable systems.
Bordered-Sutured Floer Homology as a Sutured TQFT
Explore advanced quantum topology concepts through bordered-sutured Floer homology and its applications as a sutured TQFT in this in-depth lecture by J. Rasmussen.
Parallel Decomposition of Persistence Modules Through Interval Bases
Exploring parallel decomposition of persistence modules using interval bases, with applications in Topological Data Analysis and connections to the Hodge Laplacian.
Topology of Complexes Arising in Models for Distributed Computing
Explore simplicial models in distributed computing, focusing on chromatic subdivisions and their applications to problems like Weak Symmetry Breaking, leading to new mathematical questions.
Katharine Turner - PCA of Persistent Homology Rank Functions with Case Studies
Explore persistent homology rank functions through PCA, featuring case studies and insights into topological data analysis techniques.
The Asynchronous Computability Theorem - Distributed Systems and Algebraic Topology
Explore the connection between distributed systems protocols and algebraic topology, proving consensus impossibility in asynchronous wait-free models through combinatorial structures.
Geometric Deep Learning - Graph Neural Networks and Differential Equations
Explore Graph Neural Networks, symmetry principles, and connections to differential equations, geometry, and topology in this comprehensive introduction to Geometric Deep Learning.
Shtukas and Excursions in Categorical Spectral Theory - Talk 42
Delve into advanced mathematical concepts exploring the relationship between excursion operators, shtuka cohomologies, and categorical spectral action through categorical traces.
Localizing Invariants of Large Categories: General Theory
Delve into advanced algebraic K-theory concepts, exploring dualizable stable categories, continuous K-theory applications, and their relationship with sheaf categories on Hausdorff spaces.
Localizing Motives, Algebraic KK-Theory and Refined Negative Cyclic Homology
Delve into advanced algebraic geometry concepts exploring localizing motives, their rigidity properties, and applications in refined negative cyclic homology and topological cyclic homology.
Shtukas and Global Langlands for Function Fields - Talk 37
Delve into V. Lafforgue's groundbreaking proof of global Langlands correspondence, exploring shtukas, geometric Satake, and excursion operators in function fields through expert analysis.
Overview of Restricted Geometric Langlands Theory
Delve into categorical formulations of geometric Langlands theory, exploring restricted local systems, their applications in arithmetic, and connections to automorphic forms through Frobenius traces.
Low Dimensional Topology and Circle-valued Morse Functions
Explore representations in Homeo_+(S^1) and their role in verifying left-orderability of 3-manifold groups, with applications to the L-space conjecture and taut foliations in various topological settings.
Low Dimensional Topology and Circle-valued Morse Functions
Explore instanton Floer homology's surgery formula, its applications in computing 3-manifold invariants, and connections to SU(2)-representations of fundamental groups.
The Mathematician Who Cracked Wall Street
Explore how mathematician Jim Simons applied complex math to finance, revolutionizing Wall Street and using his success to support math education and scientific research.
Relative Symplectic Cohomology of Pairs
Delve into advanced symplectic geometry concepts, focusing on relative symplectic cohomology's extension to subset pairs and its applications in demonstrating new symplectic rigidity phenomena.
Interactions and Topological Synchronization in Simplicial Kuramoto Model
Delve into the mathematical foundations of simplicial Kuramoto models, exploring oscillator dynamics, topology-geometry relationships, and synchronization patterns in complex networks.
Measuring Graph Distance Using the Labeled Merge Tree Interleaving Distance
Explore geometric graph analysis through merge trees, learning advanced techniques for measuring distances between networks using directional transforms and multi-labeling schemes.
Multiparameter Persistence for Machine Learning in Topological Data Analysis
Explore advanced Topological Data Analysis through multiparameter persistence, focusing on practical machine learning applications using MMA decomposition and signed barcode techniques.
Chern-Simons Field Theory Invariants - Knots, Links and Three-Manifolds - Part 2
Explore advanced concepts in Chern-Simons field theory, focusing on invariants of knots, links, and three-manifolds in this continuation lecture.