From the Kauffman and Dubrovnik Polynomials to Cubic Skein Modules and Beyond
Explore the rich world of skein theory, from linear and quadratic modules to the untapped potential of cubic skein modules and their connections to various mathematical disciplines.
Algebraic Presentations of 4- and 3-Manifolds in Low-Dimensional Topology
Explore algebraic presentations of 4- and 3-manifolds, focusing on categories of n-cobordisms and their relation to low-dimensional topology and combinatorial group theory.
Volume Conjecture for Surface Diffeomorphisms
Explore quantum invariants for surface diffeomorphisms and their connection to mapping torus volume. Examine representation theory, numerical evidence, and a proof for the figure-eight knot complement case.
Diagrammatics in Categories - Lecture 4
Explorez les catégories diagrammatiques en algèbre à travers des exemples concrets et leur formalisme spécifique. Développez votre compréhension des applications dans divers domaines.
Algebraization of Low-Dimensional Topology - Part II
Explore algebraic presentations of cobordism categories in 3 and 4 dimensions, focusing on torus-based structures and their implications for Topological Quantum Field Theories.
Diagrammatics in Categories - Lecture 5
Explorez les catégories diagrammatiques en algèbre à travers des exemples concrets et leur formalisme spécifique, en laissant place à la généralisation.
Affine W-algebras - Lecture 5
Explore affine W-algebras construction, theory, and applications in vertex algebra. Delve into quantum Hamiltonian reduction, Virasoro minimal models, and tensor categories of W-algebra representations.
Affine W-algebras - Part I
Explore affine W-algebras construction via quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
W-algebras and Lax Operators - Lecture 5
Explore finite W-algebras, twisted Yangians, and Lax operators. Investigate relationships between these mathematical structures in quantum algebra and integrable systems.
W-algebras and Lax Operators - Lecture 3
Explore finite W-algebras, twisted Yangians, and Lax operators. Investigate relationships between these mathematical structures using advanced algebraic techniques.
Quantization, Gauge Theory, and the Analytic Approach to Geometric by Edward Witten
Explore quantization, gauge theory, and geometric analysis with renowned physicist Edward Witten in this advanced lecture on the intersection of quantum field theory and geometric representation theory.
BPS States and 3d TQFTs
Explore the connection between BPS state counting in string theory and new 3-manifold invariants, examining recent progress and relationships with familiar topological quantum field theories.
TQFTs from Non-Semisimple Modular Categories and Modified Traces - Marco de Renzi
Explore non-semisimple TQFTs and modified traces in topology, focusing on construction methods, invariants, and mapping class group representations derived from modular categories.
Re Normalized TQFTs
Explore re-normalized Topological Quantum Field Theories with Nathan Geer, delving into advanced concepts in quantum topology and mathematical physics.
The Basics of TQFT
Explore the fundamental principles of Topological Quantum Field Theory (TQFT) in this comprehensive lecture, covering key concepts and applications in quantum topology.
State Sum Homotopy QFTs
Explore state sum homotopy quantum field theories with Alexis Virelizier, delving into advanced mathematical concepts and their applications in theoretical physics.
A Skein Theoretic Approach to CFT Correlators - Part 3
Explore advanced skein theoretic techniques for analyzing conformal field theory correlators in this in-depth mathematical physics lecture.
A Skein Theoretic Approach to CFT Correlators - Part 2
Explore skein theoretic approaches to CFT correlators in this advanced physics lecture, delving into mathematical techniques for analyzing quantum field theories.
Quantum Chern-Simons Theory: Real and Complex Formulations - Lecture 3
Explore WRT invariants, Resurgence conjecture, and Teichmüller TQFT in quantum Chern-Simons theory, with detailed examples and new formulations.
Quantum Chern-Simons Theory: Real and Complex Formulations - Lecture 2/3
Explore Quantum Chern-Simons Theory, covering WRT invariants, Resurgence conjecture, and Teichmüller TQFT, with detailed examples and discussions.
Topological Phases of Quantum Lattice Systems and Higher Berry Classes - Lecture 3
Explore recent advances in classifying gapped lattice systems and their implications for quantum matter phases, focusing on Short-Range Entangled phases and higher Berry classes.