Algebraization of Low-Dimensional Topology - Lecture 4
Explore algebraic presentations of cobordism categories in 3 and 4 dimensions, focusing on torus-based structures and their implications for Topological Quantum Field Theories.
Algebraization of Low-Dimensional Topology - Part I
Explore algebraic presentations of cobordism categories in low-dimensional topology. Learn about 3- and 4-modular Hopf algebras and their role in classifying TQFTs.
Braided Fusion Categories - Lecture 3
Explore semisimple braided tensor categories, their structure, and classification. Delve into centralizers, non-degeneracy, equivariantizations, and the core of braided fusion categories.
Introduction to Contact Geometry by Dheeraj Kulkarni
Explore contact geometry fundamentals, including Frobenius theorem, contactomorphisms, and Gray stability theorem. Learn about symplectic structures and their relation to contact manifolds.
Monica Vazirani- Representations of the Affine BMW Category
Explore Walker's TQFT-motivated construction of affine BMW category representations, their combinatorial description, and implications for affine BMW algebra representations in this advanced mathematics lecture.
TQFTs From Non-Semisimple Modular Categories and Modified Traces - Marco de Renzi
Explore advanced TQFTs, non-semisimple modular categories, and modified traces in topology. Learn about cutting-edge techniques for studying 3-manifolds and mapping class group representations.
TQFTs from Non-Semisimple Modular Categories and Modified Traces - Lecture I
Explore advanced topological quantum field theories, focusing on non-semisimple constructions and modified traces for powerful invariants and mapping class group representations.
Introduction to Chern Simons Theory and Topology
Explore Chern Simons Theory and its connections to topology with renowned physicist Edward Witten in this advanced workshop on quantum information and physics.
TQFTs and the Renaissance of the Algebraic Topology of Manifolds
Explore the resurgence of algebraic topology in manifold studies, focusing on Topological Quantum Field Theories and their impact on modern mathematical research.
Group Representations on 2D Topological Quantum Field Theories
Explore group representations in 2D topological quantum field theories, delving into advanced mathematical concepts and their applications in theoretical physics.
Exponential Networks and DT Invariants
Explore exponential networks and Donaldson-Thomas invariants in this advanced mathematics lecture, delving into complex algebraic structures and topological insights.
An Introduction to Fusion Rings - Part II
Explore advanced fusion ring concepts, their applications in physics and mathematics, and their connection to particle interactions in various dimensions. Learn computational methods for finding and analyzing fusion rings.
Open Gromov-Witten Invariants from the Fukaya Category
Explore recent progress in deriving Gromov-Witten invariants from the Fukaya category, focusing on cyclic open-closed maps, R-matrices, and potential extensions to open invariants.
Towards 2-Categorical 3D Mirror Symmetry
Explore 2-categorical aspects of 3d mirror symmetry in geometry and representation theory, focusing on boundary conditions in 3d N=4 SUSY QFTs and their connections to hyperkähler geometry.
Composition, DG-Modules, and Cobordism Maps in Bordered Floer Homology
Explore bordered Floer homology, dg-modules, and the topological interpretation of module homomorphism composition in Heegaard Floer complexes. Gain insights into cobordism maps and their consequences.
Categorical Aspects of the Fueter Equation in 3D Topological Quantum Field Theory
Explore categorical aspects of the Fueter equation, examining its role in topological quantum field theory and connections to complex geometry and mirror symmetry.
Poincare Duality and TQFT Structures for Loop Spaces
Explore Poincaré duality and TQFT structures in loop spaces, delving into advanced algebraic topology concepts with K. Cieliebak from Augsburg.
Operads and the Blob Complex in Topological Quantum Field Theory
Explorez la théorie des opérades et le complexe blob en TQFT, en examinant la résolution de barre opéradique et les catégories opéradiques unaires.
Turaev-Viro-Barrett-Westbury State Sums with Defects
Explore Turaev-Viro-Barrett-Westbury state sums with defects in quantum field theory, presented by C. Meusburger from Friedrich-Alexander-Universität.
Global Lie Theory: Wild Riemann Surfaces and Their Character Varieties
Explore the evolution of topological symplectic structures, wild Riemann surfaces, and character varieties in global Lie theory. Discover connections to quantum groups, hyperkähler geometry, and integrable systems.
Knots, Operator Algebras, and Physics - Part II
Explore advanced mathematical concepts connecting knot theory, operator algebras, and physics, focusing on Kaufman brackets and entanglement schemes.