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#Quantum Topology

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QuantumTopology

25.03.2020 Ф.Г. Кораблёв - Автоморфизмы раскрасок и инварианты узлов

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Исследование автоморфизмов раскрасок и их связи с инвариантами узлов в топологии. Анализ современных методов и подходов в этой области математики.
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1 Lesons
58 minutes
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Free-Video
QuantumTopology

9.12.2017 И.А. Дынников - Рокировочные классы прямоугольных диаграмм и лежандровы узлы

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Исследование рокировочных классов прямоугольных диаграмм и их связи с лежандровыми узлами в топологии. Анализ математических свойств и применений.
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1 Lesons
43 minutes
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Free-Video
IMSA

Quantization of Moduli Spaces of Local Systems at Roots of Unity

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Explore quantization of G-local system moduli spaces on decorated surfaces, discussing applications to quantum topology and quantum group representations.
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1 Lesons
1 hour 3 minutes
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Free-Video
QuantumTopology

A. Malutin - On Domination of Hyperbolic Knots

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Explore hyperbolic knot domination in topology, examining mathematical concepts and techniques for analyzing knot structures and their properties in hyperbolic space.
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1 Lesons
1 hour 36 minutes
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Free-Video
QuantumTopology

Pachner's 3-3 Relations and Hopf Algebras

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Explore Pachner's 3-3 relations and their connections to Hopf algebras in quantum topology, delving into advanced mathematical concepts and their applications.
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1 Lesons
49 minutes
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Free-Video
QuantumTopology

Conjugation of Global Knots

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Explore the mathematical concept of conjugation in global knots, delving into advanced topological theories and their applications in quantum mechanics.
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1 Lesons
1 hour 8 minutes
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Free-Video
QuantumTopology

On the Number of Non Hyperbolic Knots

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Explore the intriguing world of non-hyperbolic knots with Andrei Malyutin's in-depth analysis, offering insights into their quantity and mathematical properties.
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1 Lesons
46 minutes
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Free-Video
QuantumTopology

Homology of Yang-Baxter Operators and Search for (Co)Cycle Invariants of Knots

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Explore homology of Yang-Baxter operators and the quest for (co)cycle invariants in knot theory with mathematician Jozef Przytycki in this advanced topology lecture.
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1 Lesons
59 minutes
On-Demand
Free-Video
QuantumTopology

Ph. Korablev - Quantum Invariants of Knots

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Explore quantum invariants of knots, delving into advanced mathematical concepts and their applications in topology and quantum mechanics.
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1 Lesons
1 hour 26 minutes
On-Demand
Free-Video
QuantumTopology

The Stat-Sums on the Spines of Three-Dimensional Manifolds

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Explore state-sums on spines of 3D manifolds with V. Turaev, delving into advanced concepts in quantum topology and geometric structures.
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1 Lesons
1 hour 38 minutes
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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
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Free-Video
NCCR SwissMAP

Equivariant Derived Category of a Reductive Group as a Categorical Center

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Explore equivariant derived categories of reductive groups and their role as categorical centers in representation theory.
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1 Lesons
1 hour 7 minutes
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Free-Video
NCCR SwissMAP

Various Incarnations of the Affine Hecke Category

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Explorez les différentes incarnations de la catégorie de Hecke affine dans le cadre de la théorie des représentations quantiques.
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1 Lesons
46 minutes
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Free-Video
NCCR SwissMAP

Quantum Category O vs Affine Hecke Category - Lecture 1

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Explore quantum category O and affine Hecke category in representation theory with Yale University's I. Losev at the Quantum Topobology Biennial.
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1 Lesons
1 hour 10 minutes
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Free-Video
NCCR SwissMAP

Categorified Traces and Colored SL_2 Knot Homology

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Explore categorified traces and colored SL_2 knot homology in quantum topology, focusing on representation theory applications.
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1 Lesons
59 minutes
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Free-Video
NCCR SwissMAP

From Representation Theory to Topology: There and Back Again

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Explorez les liens fascinants entre la théorie des représentations et la topologie quantique dans cette conférence approfondie.
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1 Lesons
1 hour 5 minutes
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Free-Video
NCCR SwissMAP

Aha and Eha in Quantum Topology Representation Theory

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Explore representation theory in quantum topology with A. Negut from MIT, delving into Aha and Eha concepts during this insightful lecture.
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1 Lesons
59 minutes
On-Demand
Free-Video
NCCR SwissMAP

Soergel Bimodules, Matrix Factorizations and Hilbert Schemes

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Explore Soergel bimodules, matrix factorizations, and Hilbert schemes in quantum topology, focusing on representation theory applications.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Banach Center

Knot Quantum Invariants, Graphs, and Combinatorics - Part 2

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Explore advanced concepts in knot theory, focusing on quantum invariants, graph theory, and combinatorial techniques. Delve into intricate mathematical relationships.
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1 Lesons
42 minutes
On-Demand
Free-Video
Banach Center

Knots-Quivers Correspondence: Generalizations and Combinatorics

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Explore knots-quivers correspondence, its extensions, and applications in enumerative combinatorics, including lattice paths and Schröder paths counting.
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1 Lesons
1 hour 13 minutes
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Free-Video
Centre for Quantum Technologies

Topology in Time-Evolving Quantum Systems

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Delve into quantum topology's dynamic nature, exploring how symmetry changes affect topological invariants in non-equilibrium systems through experimental studies with ultracold atomic BEC in 1D lattices.
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1 Lesons
57 minutes
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Free-Video
QuantumTopology

Splitting Numbers and Signatures

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Explore number theory and topology with a focus on splitting numbers, linking number bounds, and signature results in this advanced mathematical lecture.
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8 Lesons
55 minutes
On-Demand
Free-Video
QuantumTopology

Twisted Homology and Twisted Simplical Groups - Another Approach to Quantum Topology

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Explore twisted homology and simplicial groups as alternative approaches to quantum topology, delving into advanced mathematical concepts and their applications.
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1 Lesons
40 minutes
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Free-Video
QuantumTopology

Simplified Khovanov Rozansky Calculus

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Explore simplified Khovanov Rozansky calculus with Andrey Morozov, delving into advanced quantum topology concepts and their applications in mathematical physics.
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1 Lesons
48 minutes
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Free-Video
QuantumTopology

On a High Dimensional Generalization of Seifert Fibrations

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Explore high-dimensional generalizations of Seifert fibrations, extending classical concepts to modern topological structures and manifolds.
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1 Lesons
41 minutes
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Free-Video
QuantumTopology

3 Dimensional HQFTs

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Explore 3-dimensional Homotopy Quantum Field Theories with Alexis Virelizier, delving into advanced mathematical concepts and their applications in quantum topology.
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1 Lesons
57 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 Thurston Norm of 3-Manifolds with a 2-Generator Fundamental Group

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Explore the Thurston norm in 3-manifolds with 2-generator fundamental groups, delving into advanced concepts in quantum topology and geometric group theory.
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1 Lesons
52 minutes
On-Demand
Free-Video
QuantumTopology

The Kashaev Invariant, Nahm Sums and Modularity

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Explore the Kashaev invariant, Nahm sums, and modularity in quantum topology, delving into advanced mathematical concepts and their applications.
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1 Lesons
52 minutes
On-Demand
Free-Video
QuantumTopology

Triangular Decomposition of Skein Algebras and Quantum Teichmuuller Spaces

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Explore triangular decomposition of skein algebras and quantum Teichmuller spaces in this advanced mathematical lecture by Thang Le, delving into complex topological concepts.
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1 Lesons
55 minutes
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Free-Video
QuantumTopology

E. Fominykh - Special Spines with Three 2-Components

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Explore special spines with three 2-components in topology, focusing on their unique properties and applications in quantum theory and geometric structures.
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1 Lesons
1 hour 20 minutes
On-Demand
Free-Video
QuantumTopology

A. Slepcov - Quantum Invariants of Knots and Their Properties

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Explore quantum invariants of knots, their properties, and applications in topology. Gain insights into advanced mathematical concepts and their relevance in quantum theory.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
QuantumTopology

Ph. Korablev - Yang-Baxter Operators and Invariants of Links

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Explore Yang-Baxter operators and their applications in link invariants, delving into quantum topology concepts and mathematical techniques for analyzing knot structures.
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1 Lesons
1 hour 26 minutes
On-Demand
Free-Video
QuantumTopology

On Complexity of Virtual Manifolds

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Explore virtual manifolds' complexity, focusing on theoretical aspects and mathematical implications in quantum topology research.
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1 Lesons
51 minutes
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Free-Video
QuantumTopology

Dijkgraaf-Witten Invariants Over Z2 for Twice Orientable Seifert Manifolds

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Explore Dijkgraaf-Witten invariants over Z2 for twice orientable Seifert manifolds, delving into advanced concepts in quantum topology and manifold theory.
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1 Lesons
45 minutes
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Free-Video
QuantumTopology

Matching Groups and Gliding Systems

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Explore matching groups and gliding systems in topology, delving into advanced mathematical concepts and their applications in quantum mechanics and related fields.
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1 Lesons
57 minutes
On-Demand
Free-Video
QuantumTopology

V. Tarkaev - Construction of the Khovanov Homology

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Explore the construction of Khovanov homology, a powerful invariant in knot theory, and its applications in quantum topology and low-dimensional manifolds.
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1 Lesons
1 hour 28 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)

Resurgence, Quantum Modularity and Quantum Invariants in Three-Manifolds

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Explore resurgence in quantum Chern-Simons theory, connecting WRT quantum invariants to BPS q-series. Uncover complex Chern-Simons invariants and prove quantum modularity for Seifert fibered homology spheres.
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1 Lesons
56 minutes
On-Demand
Free-Video
Kavli Institute for Theoretical Physics

Crystallization Can Create Chern Insulators

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Explore how crystallization processes can lead to the formation of Chern insulators, a unique class of topological materials, in this advanced physics talk by Dan Parker from UCSD.
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1 Lesons
42 minutes
On-Demand
Free-Video
NCCR SwissMAP

Derived Skein Modules via Factorization Homology

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Explore derived skein modules through factorization homology, delving into categorical symmetries in quantum field theory.
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1 Lesons
1 hour 15 minutes
On-Demand
Free-Video
NCCR SwissMAP

The Center of the Small Quantum Group and Affine Springer Fibers

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Explore representation theory through quantum groups and affine Springer fibers, focusing on the center of small quantum groups.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
NCCR SwissMAP

Spark Algebras and Quantum Groups

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Explore representation theory through spark algebras and quantum groups, focusing on quantum topology concepts.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
NCCR SwissMAP

Bordered-Sutured Floer Homology as a Sutured TQFT

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Explore advanced quantum topology concepts through bordered-sutured Floer homology and its applications as a sutured TQFT in this in-depth lecture by J. Rasmussen.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
NCCR SwissMAP

Heisenberg Homologies of Configurations in Ribbon Graphs

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Explore Heisenberg homologies in ribbon graffs configurations, focusing on quantum topology and representation theory.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
NCCR SwissMAP

Non-semisimple Link and Manifold Invariants

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Explore non-semisimple link and manifold invariants in quantum topology, focusing on representation theory with A. Gainutdinov from CNRS, Université de Tours.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-valued Morse Functions

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Explore Khovanov homology of torus braids, characterizing simplified complexes and their applications in quantum topology. Gain insights into recent advancements and conjectures in low-dimensional topology.
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16 Lesons
1 hour 1 minute
On-Demand
Free-Video
Banach Center

3D Quantum Trace Map: Construction and Applications in Ideally Triangulated 3-Manifolds

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Explore the construction of the 3d quantum trace map, linking Kauffman bracket skein modules to quantum gluing modules in ideally triangulated 3-manifolds.
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1 Lesons
58 minutes
On-Demand
Free-Video
ICTP-SAIFR

Spectrum of Entanglement as a Dimensional Reduction Tool for Studying Topological Insulators

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Explore entanglement spectrum as a tool for studying topological insulators, focusing on interactions and disorder in quantum materials.
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15 Lesons
42 minutes
On-Demand
Free-Video
QuantumTopology

D. Ilyutko - Chord Diagrams

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Explore chord diagrams in topology, their applications, and mathematical properties. Gain insights into this powerful tool for visualizing and analyzing complex relationships in data structures.
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1 Lesons
1 hour 26 minutes
On-Demand
Free-Video
BIMSA

Integrable Systems and Representation Theory: Between Geometry, Algebra and Analysis

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Explore integrable systems in Hamiltonian mechanics, quantum systems, and statistical mechanics. Examine connections to representation theory and gauge theory quantization.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video