Lie Algebras and Homotopy Theory - Jacob Lurie
Explore connections between Lie algebras and homotopy theory, covering fundamental groups, Whitehead brackets, and Quillen's theorem in this advanced mathematics seminar.
Univalence from a Computer Science Point-of-View - Dan Licata
Explore univalence in computer science with Dan Licata, covering Martin-Löf type theory, computation, and applications in homotopy theory and group structures.
René Thom and Semantic Information - Exploring Mathematical Approaches to Meaning
Explore René Thom's ideas on semantic information, extending beyond Shannon's statistical theory to topological dynamics and singularity theory applications in biology, linguistics, and philosophy.
Invariants for Tame Parametrised Chain Complexes
Explore invariants for tame parametrised chain complexes in applied algebraic topology, focusing on explicit constructions, comprehensive frameworks, and discriminative power in topological data analysis.
Star Clusters in Clique Complexes and the Vietoris-Rips Complex of Planar Sets
Explore star clusters in simplicial complexes and their applications to independence complexes and Vietoris-Rips complexes of planar sets, with insights on homotopy information and related conjectures.
Vietoris-Rips Thickenings - Problems for Birds and Frogs
Explore open problems in Vietoris-Rips complexes, connecting diverse mathematical areas. Suitable for both broad theorists and problem-solving specialists in applied algebraic topology.
Cubespaces and Homotopy Theory
Delve into advanced mathematical concepts exploring the intersection of cubespaces and homotopy theory, with insights from topological dynamics and ergodic theory applications.
Wall Finiteness Obstruction for DG Categories II
Exploration of Wall finiteness obstruction theorem for DG categories, including applications to phantom DG categories and derived categories of algebraic varieties. Discusses extensions to algebras over DG operads.
Wojciech Chachólski - TDA Invariants and Model Categories
Exploring TDA invariants and model categories in data analysis, focusing on simplification techniques from homotopy theory to extract meaningful summaries while balancing information retention.
Basic Homotopy Theory by Samik Basu
Explore fundamental concepts in homotopy theory, including maps, CW complexes, equivalences, and fibrations. Gain insights into key computations and sequences in this foundational area of topology.
The Transfer in Algebraic K-Theory and THH
Explore algebraic K-theory transfers, their applications in A-theory, and connections to THH. Gain insights into fundamental questions and trace methods in this advanced mathematics lecture.
Artin Reciprocity via Spheres
Explore Artin reciprocity through spheres, covering functionality, logical construction, global fields, spectra, and K theory in this advanced mathematics lecture.
Homotopic Distance and Generalized Motion Planning
Explore homotopic distance between maps, unifying Lusternik-Schnirelmann category and topological complexity. Learn how Morse-Bott functions and navigation functions apply to generalized motion planning problems.
Homotopy Types of Vietoris–Rips Complexes of Metric Gluings
Explore homotopy types of Vietoris-Rips complexes in metric wedge sums and gluings, with applications to persistent homology of metric graphs and insights into open research directions.
A Counter-Example to Hausmann's Conjecture
Explore a counter-example to Hausmann's conjecture on Vietoris-Rips complexes, challenging long-held beliefs in algebraic topology using persistent homology.
Persistent Homotopy Groups of Metric Spaces
Exploring persistent homotopy groups of metric spaces, blending topology and geometry to capture dataset features beyond persistent homology, with applications and stability properties.
Motivic Cohomology - Past, Present and Future
Explore motivic cohomology's evolution, recent developments, and future prospects in algebraic geometry, including cycles with modulus and Chow-Witt theory.
Topology - Lecture 13
Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.
Topology - Lecture 20
Explore advanced concepts in topology, including complex mathematical structures and their properties, in this comprehensive lecture by Bruno Zimmerman.
Topology - Lecture 12
Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.
Topology - Lecture 16
Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.