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#Topological Quantum Field Theory

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Centre de recherches mathématiques - CRM

Algebraization of Low-Dimensional Topology - Lecture 4

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Explore algebraic presentations of cobordism categories in 3 and 4 dimensions, focusing on torus-based structures and their implications for Topological Quantum Field Theories.
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1 Lesons
57 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Algebraization of Low-Dimensional Topology - Part I

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Explore algebraic presentations of cobordism categories in low-dimensional topology. Learn about 3- and 4-modular Hopf algebras and their role in classifying TQFTs.
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1 Lesons
57 minutes
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Free-Video
Centre de recherches mathématiques - CRM

Braided Fusion Categories - Lecture 3

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Explore semisimple braided tensor categories, their structure, and classification. Delve into centralizers, non-degeneracy, equivariantizations, and the core of braided fusion categories.
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1 Lesons
53 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Introduction to Contact Geometry by Dheeraj Kulkarni

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Explore contact geometry fundamentals, including Frobenius theorem, contactomorphisms, and Gray stability theorem. Learn about symplectic structures and their relation to contact manifolds.
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20 Lesons
1 hour 27 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Monica Vazirani- Representations of the Affine BMW Category

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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.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

TQFTs From Non-Semisimple Modular Categories and Modified Traces - Marco de Renzi

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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.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

TQFTs from Non-Semisimple Modular Categories and Modified Traces - Lecture I

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Explore advanced topological quantum field theories, focusing on non-semisimple constructions and modified traces for powerful invariants and mapping class group representations.
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1 Lesons
1 hour 5 minutes
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Free-Video
Institute for Advanced Study

Introduction to Chern Simons Theory and Topology

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Explore Chern Simons Theory and its connections to topology with renowned physicist Edward Witten in this advanced workshop on quantum information and physics.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
Fields Institute

TQFTs and the Renaissance of the Algebraic Topology of Manifolds

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Explore the resurgence of algebraic topology in manifold studies, focusing on Topological Quantum Field Theories and their impact on modern mathematical research.
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1 Lesons
43 minutes
On-Demand
Free-Video
Dublin Institute for Advanced Studies DIAS

Group Representations on 2D Topological Quantum Field Theories

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Explore group representations in 2D topological quantum field theories, delving into advanced mathematical concepts and their applications in theoretical physics.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Exponential Networks and DT Invariants

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Explore exponential networks and Donaldson-Thomas invariants in this advanced mathematics lecture, delving into complex algebraic structures and topological insights.
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1 Lesons
1 hour 16 minutes
On-Demand
Free-Video
Dublin Institute for Advanced Studies DIAS

An Introduction to Fusion Rings - Part II

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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.
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1 Lesons
2 hours 25 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Open Gromov-Witten Invariants from the Fukaya Category

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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.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Towards 2-Categorical 3D Mirror Symmetry

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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.
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1 Lesons
2 hours 10 minutes
On-Demand
Free-Video
Western Hemisphere Virtual Symplectic Seminar

Composition, DG-Modules, and Cobordism Maps in Bordered Floer Homology

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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.
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1 Lesons
45 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Categorical Aspects of the Fueter Equation in 3D Topological Quantum Field Theory

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Explore categorical aspects of the Fueter equation, examining its role in topological quantum field theory and connections to complex geometry and mirror symmetry.
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18 Lesons
1 hour 30 minutes
On-Demand
Free-Video
NCCR SwissMAP

Poincare Duality and TQFT Structures for Loop Spaces

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Explore Poincaré duality and TQFT structures in loop spaces, delving into advanced algebraic topology concepts with K. Cieliebak from Augsburg.
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1 Lesons
56 minutes
On-Demand
Free-Video
Institut Henri Poincaré

Operads and the Blob Complex in Topological Quantum Field Theory

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Explorez la théorie des opérades et le complexe blob en TQFT, en examinant la résolution de barre opéradique et les catégories opéradiques unaires.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
NCCR SwissMAP

Turaev-Viro-Barrett-Westbury State Sums with Defects

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Explore Turaev-Viro-Barrett-Westbury state sums with defects in quantum field theory, presented by C. Meusburger from Friedrich-Alexander-Universität.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Global Lie Theory: Wild Riemann Surfaces and Their Character Varieties

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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.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Banach Center

Knots, Operator Algebras, and Physics - Part II

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Explore advanced mathematical concepts connecting knot theory, operator algebras, and physics, focusing on Kaufman brackets and entanglement schemes.
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7 Lesons
2 hours 8 minutes
On-Demand
Free-Video
Banach Center

From the Kauffman and Dubrovnik Polynomials to Cubic Skein Modules and Beyond

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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.
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1 Lesons
53 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Algebraic Presentations of 4- and 3-Manifolds in Low-Dimensional Topology

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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.
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1 Lesons
53 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Volume Conjecture for Surface Diffeomorphisms

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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.
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1 Lesons
54 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Diagrammatics in Categories - Lecture 4

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Explorez les catégories diagrammatiques en algèbre à travers des exemples concrets et leur formalisme spécifique. Développez votre compréhension des applications dans divers domaines.
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1 Lesons
52 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Algebraization of Low-Dimensional Topology - Part II

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Explore algebraic presentations of cobordism categories in 3 and 4 dimensions, focusing on torus-based structures and their implications for Topological Quantum Field Theories.
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1 Lesons
49 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Diagrammatics in Categories - Lecture 5

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Explorez les catégories diagrammatiques en algèbre à travers des exemples concrets et leur formalisme spécifique, en laissant place à la généralisation.
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1 Lesons
51 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Affine W-algebras - Lecture 5

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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.
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1 Lesons
45 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Affine W-algebras - Part I

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Explore affine W-algebras construction via quantum Hamiltonian reduction. Delve into vertex algebra theory, Virasoro minimal models, and tensor categories of W-algebra representations.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

W-algebras and Lax Operators - Lecture 5

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Explore finite W-algebras, twisted Yangians, and Lax operators. Investigate relationships between these mathematical structures in quantum algebra and integrable systems.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

W-algebras and Lax Operators - Lecture 3

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Explore finite W-algebras, twisted Yangians, and Lax operators. Investigate relationships between these mathematical structures using advanced algebraic techniques.
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1 Lesons
40 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Quantization, Gauge Theory, and the Analytic Approach to Geometric by Edward Witten

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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.
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1 Lesons
1 hour 19 minutes
On-Demand
Free-Video
IMSA

BPS States and 3d TQFTs

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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.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

TQFTs from Non-Semisimple Modular Categories and Modified Traces - Marco de Renzi

0 rewiews
Explore non-semisimple TQFTs and modified traces in topology, focusing on construction methods, invariants, and mapping class group representations derived from modular categories.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
QuantumTopology

Re Normalized TQFTs

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Explore re-normalized Topological Quantum Field Theories with Nathan Geer, delving into advanced concepts in quantum topology and mathematical physics.
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1 Lesons
55 minutes
On-Demand
Free-Video
QuantumTopology

The Basics of TQFT

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Explore the fundamental principles of Topological Quantum Field Theory (TQFT) in this comprehensive lecture, covering key concepts and applications in quantum topology.
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1 Lesons
1 hour 33 minutes
On-Demand
Free-Video
Galileo Galilei Institute

State Sum Homotopy QFTs

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Explore state sum homotopy quantum field theories with Alexis Virelizier, delving into advanced mathematical concepts and their applications in theoretical physics.
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Galileo Galilei Institute

A Skein Theoretic Approach to CFT Correlators - Part 3

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Explore advanced skein theoretic techniques for analyzing conformal field theory correlators in this in-depth mathematical physics lecture.
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1 Lesons
1 hour 45 minutes
On-Demand
Free-Video
Galileo Galilei Institute

A Skein Theoretic Approach to CFT Correlators - Part 2

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Explore skein theoretic approaches to CFT correlators in this advanced physics lecture, delving into mathematical techniques for analyzing quantum field theories.
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1 Lesons
1 hour 47 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Quantum Chern-Simons Theory: Real and Complex Formulations - Lecture 3

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Explore WRT invariants, Resurgence conjecture, and Teichmüller TQFT in quantum Chern-Simons theory, with detailed examples and new formulations.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Quantum Chern-Simons Theory: Real and Complex Formulations - Lecture 2/3

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Explore Quantum Chern-Simons Theory, covering WRT invariants, Resurgence conjecture, and Teichmüller TQFT, with detailed examples and discussions.
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1 Lesons
1 hour 14 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Topological Phases of Quantum Lattice Systems and Higher Berry Classes - Lecture 3

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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.
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1 Lesons
1 hour 46 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Topological Phases of Quantum Lattice Systems and Higher Berry Classes - Lecture 2

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Explore advanced concepts in topological phases of quantum lattice systems, including higher Berry classes, SRE phases, and their classification using TQFT and homotopy groups.
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15 Lesons
1 hour 50 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Topological Phases of Quantum Lattice Systems and Higher Berry Classes - Lecture 1

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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.
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1 Lesons
1 hour 34 minutes
On-Demand
Free-Video
Galileo Galilei Institute

3D Modularity Revisited - Defect 3-Manifold Invariants and VOAs

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Explore 3D modularity, defect 3-manifold invariants, and vertex operator algebras in this advanced mathematical lecture by Ioana Coman.
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1 Lesons
51 minutes
On-Demand
Free-Video
M-Seminar, Kansas State University

Non-semisimple TQFTs from 3D N=4 Quantum Field Theories - Part 1

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Explore non-semisimple TQFTs from 3D supersymmetric field theories, examining their connections to quantum groups and vertex operator algebras in topological quantum field theory.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

VOAs from Higher-Dimensional Quantum Field Theories - Lecture 3

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Explorez les algèbres d'opérateurs vertex issues des théories quantiques des champs en dimensions supérieures et leurs liens avec d'autres domaines mathématiques.
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1 Lesons
1 hour 16 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

VOAs from Higher-Dimensional Quantum Field Theories - Lecture 4

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Explorez les algèbres d'opérateurs vertex issues des théories quantiques des champs en dimensions supérieures et leurs liens avec d'autres domaines mathématiques.
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1 Lesons
1 hour 16 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

VOAs from Higher-Dimensional Quantum Field Theories - Part I

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Explore vertex operator algebras from quantum field theories in 2-6 dimensions, focusing on connections to other mathematical branches.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

VOAs from Higher-Dimensional Quantum Field Theories - Lecture 2

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Explorez les algèbres d'opérateurs vertex issues des théories quantiques des champs en dimensions supérieures, en mettant l'accent sur leurs liens avec d'autres domaines mathématiques.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Braided Fusion Categories - Lecture 5: Witt Equivalence and Categorical Witt Group

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Explore advanced concepts in braided fusion categories, including gauging, Picard groups, Witt equivalence, and categorical Witt groups. Suitable for graduate-level mathematics students.
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1 Lesons
50 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Braided Fusion Categories - Lecture 4

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Explore algebraic theory of semisimple braided tensor categories, covering properties, examples, centralizers, equivariantizations, gauging, and Witt equivalence. Suitable for graduate students.
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9 Lesons
50 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Braided Fusion Categories - Lecture 2

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Explore algebraic theory of semisimple braided tensor categories, covering structure, classification, and applications in quantum symmetries and topological quantum field theories.
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11 Lesons
53 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Braided Fusion Categories - Lecture 1

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Explore semisimple braided tensor categories, their structure, and classification. Learn about centralizers, non-degeneracy, equivariantizations, gauging, and Witt equivalence in fusion categories.
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1 Lesons
57 minutes
On-Demand
Free-Video
Simons Institute

Polynomial-Time Preparation of Low-Temperature Gibbs States for 2D Toric Code

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Delve into quantum algorithms and mathematical techniques for preparing low-temperature Gibbs states in 2D toric code systems, focusing on polynomial-time computational methods.
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1 Lesons
36 minutes
On-Demand
Free-Video
Banach Center

Chern-Simons Field Theory Invariants - Knots, Links and Three-Manifolds - Part 1

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Explore Chern-Simons field theory invariants and their applications to knots, links, and three-manifolds in this advanced mathematics lecture.
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1 Lesons
52 minutes
On-Demand
Free-Video
Banach Center

Chern-Simons Field Theory Invariants - Knots, Links and Three-Manifolds - Part 2

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Explore advanced concepts in Chern-Simons field theory, focusing on invariants of knots, links, and three-manifolds in this continuation lecture.
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1 Lesons
51 minutes
On-Demand
Free-Video
Banach Center

Chern-Simons Field Theory Invariants - Knots, Links and Three-Manifolds - Part 3

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Explore Chern-Simons field theory invariants, focusing on knots, links, and three-manifolds in this advanced mathematical lecture.
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1 Lesons
44 minutes
On-Demand
Free-Video
Banach Center

Chern-Simons Field Theory Invariants - Knots, Links and Three-Manifolds - Part 4

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Explore Chern-Simons field theory invariants, focusing on knots, links, and three-manifolds in this advanced mathematics lecture by Ramadevi Pichai.
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1 Lesons
46 minutes
On-Demand
Free-Video
Banach Center

Chern-Simons Field Theory Invariants - Knots, Links and Three-Manifolds - Part 5

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Explore Chern-Simons field theory invariants, focusing on knots, links, and three-manifolds in this advanced mathematics lecture by Ramadevi Pichai.
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1 Lesons
52 minutes
On-Demand
Free-Video
BIMSA

Topological Defect Lines and TQFTs

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Explore topological defect lines and TQFTs with Associate Professor Babak Haghighat, delving into string theory, quantum field theory, and topological field theory concepts.
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1 Lesons
54 minutes
On-Demand
Free-Video
BIMSA

Alterfold Topological Quantum Field Theory

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Explore the connection between injective ground states of gapped Hamiltonians and TQFT, bridging topological orders with constructive quantum field theory.
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1 Lesons
50 minutes
On-Demand
Free-Video
ICTP-SAIFR

Entanglement and Holographic States in Chern-Simons Theory

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Explore entanglement and holographic states in Chern-Simons theory, covering quantum concepts, complex topology, and information paradoxes.
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24 Lesons
55 minutes
On-Demand
Free-Video
BIMSA

Gauge Fields and Categorification of Quantum Group Invariants of 3-Manifolds

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Explore new link and 3-manifold invariants associated with Verma modules of U_q(sl_N), their properties, and potential categorification in 3-manifold homology.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
BIMSA

P-Form Symmetries in Functorial Quantum Field Theory

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Explore p-form symmetries in functorial quantum field theory, focusing on implementing finite group global and gauged symmetries in TQFT using cohomology-decorated bordisms.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
BIMSA

Higher Condensation Theory in Topological Orders

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Explore a unified mathematical theory of defect condensations in topological orders across all dimensions, based on higher categories, algebras, and representations.
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1 Lesons
1 hour 13 minutes
On-Demand
Free-Video
BIMSA

Alterfold Theory for TQFT and Topological Orders in All Dimensions

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Explore alterfold theory for TQFT and topological orders across dimensions. Discover unified framework for representing concepts and generalizing results in intuitive ways.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Prague Mathematical Physics Seminar

T-duality as a Courant Algebroid Relation

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Explore exact Courant algebroids, CA relations, and generalized metrics in this mathematical physics seminar, laying groundwork for Poisson-Lie T-duality discussions.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video