A Classical View on Derived Algebraic Geometry
Explore derived algebraic geometry from a classical perspective, gaining insights into this advanced mathematical field and its applications.
Homological Algebraic Geometry
Explore semiorthogonal decompositions in algebraic geometry, including their properties, geometric significance, and novel applications in categorical constructions and singularity resolutions.
Classification of Modular Fusion Categories - Part 1 of 2 - IPAM at UCLA
Explore unitary modular tensor categories and their role in classifying topological phases of matter, covering known results, open problems, and techniques from various mathematical fields.
Stable Pair Invariants and Derived Categories - Lecture 1
Explore stable pair invariants and derived categories in mathematics with expert Y. Toda in this comprehensive lecture from ICTP Mathematics.
Ambidexterity I by Neil Strickland
Explore duality phenomena in algebraic topology, commutative algebra, and modular representation theory. Learn about derived categories, triangulated structures, and Grothendieck duality theory in this advanced mathematics lecture.
The Joy of Abstract Mathematical Thinking - With Eugenia Cheung
Explore abstract mathematical thinking through category theory, discovering its applications in everyday life, inequalities, and current events. Gain insights into abstraction, context, and relationships in mathematics.
The Zappa-Szép Product of a Fell Bundle and a Groupoid
Explore the mathematical concept of Zappa-Szép products, focusing on their application to Fell bundles and groupoids. Gain insights into advanced algebraic structures and their properties.
Triposes and Gödel's Dialectica Interpretation
Exploring semantic presentation of Gödel's Dialectica interpretation using triposes, addressing previous work and suggesting solutions to related questions in mathematical logic.
Soergel Bimodules and the Carlsson-Mellit Algebra
Explores categorical analogues of symmetric functions, focusing on Soergel bimodules and their connection to the Carlsson-Mellit algebra action in algebraic topology and representation theory.
Perverse Sheaves and Schobers on Riemann Surfaces - Tobias Dyckerhoff
Explore derived constructible categories on stratified Riemann surfaces, t-structures, Verdier duality, and categorified perverse sheaves with applications in algebraic geometry and topology.
From Hall Algebras to Legendrian Skein Algebras
Explore the connection between Hall algebras and skein algebras, delving into legendrian knot theory and Fukaya categories of surfaces. Gain insights into cutting-edge mathematical research.
Introduction to Fukaya Categories - James Pascaleff
Explore examples of Fukaya categories, focusing on surfaces and potentially other cases, building upon previous lectures on symplectic geometry and Floer cohomology.
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.
Introduction to A-Infinity Structures - Bernhard Keller
Explore A-infinity algebras, modules, and derived categories. Learn about topological origins, minimal models, and twisted objects in this advanced mathematics lecture.
Introduction to A-Infinity Structures - Bernhard Keller
Explore A-infinity algebras, their modules, and derived categories. Learn about topological origins, definitions, morphisms, bar construction, and Kadeishvili's theorem on minimal models.
Residues and Trace Maps in Grothendieck Duality - Lecture 3
Explores residues and trace maps in Grothendieck duality theory, advancing understanding of algebraic geometry and commutative algebra concepts for researchers and advanced students.
Gorenstein Duality in Topology - Lecture 3
Explore Gorenstein duality in topology, examining its connections to algebraic geometry and representation theory. Gain insights into advanced mathematical concepts and their applications.
Gorenstein Duality in Topology - Lecture 2
Explore Gorenstein duality in topology, connecting algebraic concepts to topological structures and generalizing Poincaré duality for manifolds in this advanced mathematical lecture.
Duality and Stratification in Commutative Algebra - Lecture 2
Explore duality and stratification in commutative algebra, focusing on derived categories, triangulated structures, and connections to algebraic topology and representation theory.
Ambidexterity in Topology and Algebra - Lecture 2
Explore ambidexterity in topology and algebra, focusing on duality phenomena and classification problems in tensor-triangulated categories. Gain insights into advanced mathematical concepts and their applications.
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.