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University of Oxford

Knotty Problems - Marc Lackenby

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Explore knot theory, topology, and unsolved mathematical problems with Professor Marc Lackenby in this engaging lecture on the fascinating world of knots and their applications.
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12 Lesons
52 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

The Shape of Relations: Knots and Other Stories in Topological Data Analysis

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Explore the fascinating world of Topological Data Analysis in this 59-minute conference talk by Radmila Sazdanovic, presented by the Applied Algebraic Topology Network. Discover how TDA tools can uncover relevant features in data by analyzing the shape o…
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1 Lesons
59 minutes
On-Demand
Free-Video
Institute for Advanced Study

Primes and Knots - Akshay Venkatesh

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Explore surprising parallels between number theory and 3D geometry, uncovering connections that continue to shape mathematical research.
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13 Lesons
51 minutes
On-Demand
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
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

A Álgebra de Nós

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Explore a fascinante álgebra de nós com o pesquisador Jethro van Ekeren. Descubra como essa área da matemática conecta topologia e álgebra, revelando insights surpreendentes sobre estruturas geométricas.
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1 Lesons
41 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Khovanov-Seidel Braids Representation

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Explore Khovanov-Seidel braids representation in this mathematical conference talk. Gain insights into current trends in representation theory, cluster algebras, and geometry.
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1 Lesons
55 minutes
On-Demand
Free-Video
Open Data Science

From Hyperbolic Geometry to Data Clustering

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Explore how hyperbolic geometry and knot theory inspire innovative data clustering algorithms, bridging abstract mathematics with practical data science applications.
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18 Lesons
39 minutes
On-Demand
Free-Video
Insights into Mathematics

Knots and Surfaces I - Algebraic Topology - NJ Wildberger

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Explore knot theory's origins, basic concepts, and key invariants in this introductory lecture on algebraic topology, covering Reidemeister moves, crossing numbers, and the Alexander-Conway polynomial.
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8 Lesons
52 minutes
On-Demand
Free-Video
IMSA

Crossing Numbers of Whitehead Doubles

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Explore the connection between colored Jones polynomials and crossing numbers of Whitehead doubles, revealing insights into satellite knots' minimum crossing numbers.
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8 Lesons
57 minutes
On-Demand
Free-Video
QuantumTopology

On Knot Theoretical Counterpart of the Groups G^k_n

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Explore knot theory's connection to groups G^k_n, covering tetrahedron relations, permutations, and invariants. Gain insights into geometry, topology, and group theory applications.
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19 Lesons
53 minutes
On-Demand
Free-Video
QuantumTopology

Picture Valued Invariants, Groups, and Applications of Virtual Knot Theory

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Explore picture valued invariants, groups, and applications of virtual knot theory with Professor Vassily Manturov in this advanced mathematics lecture.
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11 Lesons
55 minutes
On-Demand
Free-Video
IMSA

Skein Exact Triangles in Equivariant Singular Instanton Theory

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Explore knot signatures and singular instanton homology, focusing on skein exact triangles in equivariant theory. Uncover new insights into link invariants and their categorifications.
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18 Lesons
59 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Knot Polynomials from Chern-Simons Field Theory and Their String Theoretic Implications by P. Ramadevi

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Explore knot polynomials, Chern-Simons theory, and string theory connections. Learn about knot classification, invariants, homology, and gauge-string duality in topological strings. Discover M-theory descriptions and brane constructions.
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56 Lesons
1 hour 11 minutes
On-Demand
Free-Video
International Centre for Theoretical Sciences

Topological Strings, Knots, and Quivers - Lecture 1

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Explore topological strings, knots, and quivers in this lecture covering knot invariants, Chern-Simons theory, A-polynomials, volume conjectures, and knot homology, with exercises and examples.
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22 Lesons
1 hour 14 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Using Machine Learning to Formulate Mathematical Conjectures - IPAM at UCLA

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Explore how machine learning aids mathematicians in formulating conjectures, focusing on a discovery linking low-dimensional topology and geometry, with insights on the method's potential and limitations.
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10 Lesons
51 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Parameterized Complexity of Quantum Invariants of Knots

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Explore quantum invariants of knots, their parameterized complexity, and efficient algorithms for computation using graphical calculus and tree embeddings.
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9 Lesons
50 minutes
On-Demand
Free-Video
ICTP Mathematics

Standard and Less Standard Asymptotic Methods - Lecture 5

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Explore advanced asymptotic methods for evaluating infinite sums and sequences, including Euler-Maclaurin formula variants and less conventional techniques, with practical examples and applications.
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14 Lesons
1 hour 40 minutes
On-Demand
Free-Video
IMSA

Ribbon Concordances and Slice Obstructions: Experiments and Examples

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Explore ribbon concordances between knots, computational methods, and results in low-dimensional topology. Joint work with Nathan Dunfield on slice obstructions and experimental approaches.
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1 Lesons
46 minutes
On-Demand
Free-Video
IMSA

Rational Slice Genus Bounds from Knot Floer Homology

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Exploring rational slice genus of knots using relative adjunction inequalities and knot Floer homology, with applications to Floer simple knots and insights from 4-dimensional topology.
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1 Lesons
1 hour
On-Demand
Free-Video
IMSA

Characterizing Slopes for Alternating Knots

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Exploration des pentes caractérisantes pour les nœuds alternés, examinant leur unicité lors de chirurgies rationnelles et discutant des progrès récents dans ce domaine de la topologie.
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1 Lesons
56 minutes
On-Demand
Free-Video
IMSA

Four-Genus Bounds from the 10/8+4 Theorem

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Explore knot slicing obstructions and four-ball genus bounds using the 10/8+4 theorem. Learn about advanced techniques in gauge theory and low-dimensional topology.
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1 Lesons
58 minutes
On-Demand
Free-Video
IMSA

Quasipositive Surfaces and Decomposable Lagrangians in Topology - IMSA Seminar

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Explore Legendrian links, knot Floer homology, and Lagrangian link cobordisms in topology. Learn about braiding techniques and the comultiplication property in this advanced mathematical seminar.
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1 Lesons
53 minutes
On-Demand
Free-Video
IMSA

Symmetric Unions and Ribbon Knots

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Explore symmetric unions in knot theory, focusing on ribbon knots. Learn about classification, composite types, and infinite families of ribbon knots that defy simple symmetric union diagrams.
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9 Lesons
1 hour 2 minutes
On-Demand
Free-Video
IMSA

Welded Tangles and a Topological Interpretation of the Kashiwara-Vergne Group

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Explores welded tangles and foams as higher-dimensional knot theory, connecting their automorphisms to the Kashiwara-Vergne group in Lie theory and relating to knot invariants and Baker-Campbell-Hausdorff series.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
IMSA

The Average Genus of a 2-Bridge Knot Grows Linearly with Respect to Crossing Number

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Explore the linear growth relationship between Seifert genus and crossing number in 2-bridge knots using Chebyshev billiard table diagrams, building on previous research and experimental data.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
IMSA

Braidings and Braid Equivalences

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Explore braiding algorithms and braid equivalences for various knot types, including classical, virtual, and singular, with a focus on knotoids and braidoids.
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1 Lesons
1 hour
On-Demand
Free-Video
IMSA

Alexander Polynomials of Algebraic Links

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Explore Alexander polynomials of algebraic links, their definitions, examples, and connections to algebraic geometry. Discover the relationship between plane curve singularity spectra and link polynomials.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
International Mathematical Union

The Beauty of Braids - From Knot Invariants to Higher Categories

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Explore the fascinating world of braids, knot invariants, and higher categories in mathematics with insights from renowned expert Catharina Stroppel.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
QuantumTopology

Khovanov Homology for Knots in Thickened Torus

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Explore Khovanov homology for knots in thickened torus, delving into advanced topological concepts and their applications in quantum topology.
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1 Lesons
1 hour 35 minutes
On-Demand
Free-Video
ICTP Mathematics

From Knots to Number Theory I

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Explore connections between quantum knot invariants and number theory, covering hyperbolic topology, Kashaev invariant, and quantum modularity. No prior knowledge required.
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1 Lesons
1 hour 33 minutes
On-Demand
Free-Video
ICTP Mathematics

Some Classical Invariants of Links and Their Higher-Dimensional Analogues

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Explore geometric invariants of links and knots, including higher-dimensional analogues, with examples of non-trivial cases in ambient isotopy.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
ICTP Mathematics

Khovanov Homology and Strongly Invertible Knots

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Explore Khovanov homology's applications to strongly invertible knots, uncovering new insights in knot theory and topology.
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1 Lesons
50 minutes
On-Demand
Free-Video
ICTP Mathematics

Classification of Link Floer and Khovanov Multicurve Invariants

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Explore the classification of link Floer and Khovanov multicurve invariants in topology, presented by Claudius Zibrowius from the University of Regensburg.
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1 Lesons
53 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

From Hall Algebras to Legendrian Skein Algebras

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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.
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1 Lesons
1 hour 1 minute
On-Demand
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
On-Demand
Free-Video
QuantumTopology

Colored Graphs and Complements of Knots and Links

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Explore 4-colored graphs and their relationship to knot and link complements, delving into topological concepts and graph theory applications in knot theory.
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1 Lesons
45 minutes
On-Demand
Free-Video
QuantumTopology

Knot Invariants Arising from Homological Operations on Khovanov Homology

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Explore advanced knot theory through homological operations on Khovanov homology, uncovering new invariants and their applications in quantum topology.
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1 Lesons
50 minutes
On-Demand
Free-Video
QuantumTopology

A. Akimova - Homologically Trivial Knots in Thickened Surfaces

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Explore homologically trivial knots in thickened surfaces, examining their properties and implications for quantum topology research.
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1 Lesons
1 hour 31 minutes
On-Demand
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
On-Demand
Free-Video
QuantumTopology

A. Akimova - Homologically Trivial Knots

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Explore homologically trivial knots in quantum topology, delving into advanced mathematical concepts and their implications for knot theory and related fields.
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1 Lesons
1 hour 23 minutes
On-Demand
Free-Video
QuantumTopology

Connections of Knotoids and Knots in Thickened Torus

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Explore connections between knotoids and knots in thickened torus, delving into advanced concepts in quantum topology and geometric knot theory.
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1 Lesons
1 hour 19 minutes
On-Demand
Free-Video
QuantumTopology

Ph. Korablev - Skein-Invariants of 3-Manifolds

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Explore skein-invariants of 3-manifolds in this advanced topology lecture, delving into complex mathematical concepts and their applications in quantum topology.
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1 Lesons
1 hour 27 minutes
On-Demand
Free-Video
QuantumTopology

HOMFLY Polynomial for Rational Knots

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Explore the HOMFLY polynomial's application to rational knots, delving into advanced knot theory concepts and their mathematical implications.
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1 Lesons
1 hour 34 minutes
On-Demand
Free-Video
QuantumTopology

Cocyclic Invariants of Knots

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Explore cocyclic invariants of knots, delving into advanced mathematical concepts and their applications in quantum topology.
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1 Lesons
1 hour 30 minutes
On-Demand
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
On-Demand
Free-Video
QuantumTopology

Matroids, Delta Matroids, and Knot Invariants

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Explore matroids, delta matroids, and their applications in knot theory with Sergei Lando. Gain insights into these mathematical structures and their role in understanding knot invariants.
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1 Lesons
56 minutes
On-Demand
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

Y. Ilyina - Invariants of Knotoids

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Explore invariants of knotoids, a mathematical concept in knot theory, with Y. Ilyina's in-depth presentation on quantum topology and its applications.
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1 Lesons
1 hour 18 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

V. Tarkaev - The Complexity of an Infinite Series of Knots in the Thickened Torus

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Explore the intricacies of knot theory as V. Tarkaev delves into the complexity of infinite knot series within a thickened torus, offering insights into advanced topological concepts.
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1 Lesons
1 hour 26 minutes
On-Demand
Free-Video
QuantumTopology

A. Akimova - Classification of Prime Virtual Knots of Genus 1 With Low Complexity

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Classification methods for prime virtual knots of genus 1, focusing on those with low complexity. Explores advanced concepts in knot theory and topology.
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1 Lesons
1 hour 21 minutes
On-Demand
Free-Video
QuantumTopology

HOMFLY Polynomials for Virtual Knots

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Explore HOMFLY polynomials for virtual knots, delving into advanced concepts in quantum topology and knot theory.
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1 Lesons
53 minutes
On-Demand
Free-Video
QuantumTopology

A Normal Form for Highly Twisted Knots

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Explore a novel normal form for highly twisted knots, delving into advanced concepts in quantum topology and knot theory.
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1 Lesons
52 minutes
On-Demand
Free-Video
QuantumTopology

Classification of Prime Genus 1 Virtual Knots of Low Complexity

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Explore prime genus 1 virtual knots of low complexity, their classification methods, and implications in quantum topology with A. Akimova's in-depth analysis.
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1 Lesons
51 minutes
On-Demand
Free-Video
IMSA

Hans Boden, McMaster University - Virtual Knots and Algebraic Concordance

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Explore virtual knots, concordance groups, and new invariants using mock Seifert matrices. Discover algebraic structures and open problems in knot theory.
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1 Lesons
1 hour
On-Demand
Free-Video
Insights into Mathematics

Knots and Surfaces - Seifert Surfaces in Algebraic Topology - Lecture 2

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Explore Seifert surfaces, their construction for knots like the trefoil, and learn about Euler numbers for surfaces with boundaries in this advanced algebraic topology lecture.
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8 Lesons
38 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Constructing Knots with Specified Geometric Limits

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Explore constructive proofs for geometric limits of knot complements using circle packings on conformal boundaries of tame hyperbolic 3-manifolds, with insights on related open questions.
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1 Lesons
52 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Geometric Objects Associated to Planar Bipartite Graphs

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Explore topological and geometric data associated with planar bipartite graphs, including knots, cluster varieties, and critical varieties, and their interconnections.
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1 Lesons
50 minutes
On-Demand
Free-Video
IMSA

Knot Theory in Mathematics and AI Applications

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Explore the fascinating world of knot theory and its connections to mathematics and AI in this engaging talk by Ernesto Lupercio from CINVESTAV.
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1 Lesons
1 hour 2 minutes
On-Demand
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
Applied Algebraic Topology Network

Topological Problems Associated with DNA Nanostructures

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Explore topological challenges in DNA nanostructures, from graph theory in strand routing to knot theory in 3D embeddings. Gain insights into the emerging field of DNA mathematics and its applications.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Dublin Institute for Advanced Studies DIAS

Learning 4-Dimensional Knot Invariants from the Jones Polynomial

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Explore machine learning techniques in knot theory, focusing on learning 4D topological invariants from the Jones polynomial and their implications for understanding knot structures.
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1 Lesons
1 hour 48 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
Galileo Galilei Institute

HOMFLYPT Skein Curve Counts and Recursions

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Explore HOMFLYPT skein theory, curve counting, and recursive techniques in knot theory with insights from Tobias Ekholm's advanced mathematical lecture.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Galileo Galilei Institute

HOMFLYPT - Skein Curve Counts and Recursions

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Explore advanced mathematical concepts in skein theory, focusing on curve counts and recursive techniques in topology and knot theory.
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1 Lesons
1 hour 12 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Abelianization of Skein Modules

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Explore the mathematical concept of abelianization in skein modules, delving into advanced algebraic topology and knot theory principles.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Introduction to BPS Spectra and Quantum Invariants - Lecture 2

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Explore BPS spectra and quantum invariants in theoretical physics, delving into advanced mathematical concepts and their applications in modern quantum theory.
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1 Lesons
1 hour 32 minutes
On-Demand
Free-Video
Galileo Galilei Institute

Introduction to BPS Spectra and Quantum Invariants - Lecture 3

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Explore BPS spectra and quantum invariants in theoretical physics, delving into advanced mathematical concepts and their applications in modern quantum theory.
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1 Lesons
1 hour 45 minutes
On-Demand
Free-Video
Dublin Institute for Advanced Studies DIAS

Knots and Knotted Vortices

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Explore the fascinating world of knots and knotted vortices in this engaging public lecture by Louis Kauffman, delving into their mathematical and physical properties.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
NCCR SwissMAP

Rational Homotopy of Embedding Spaces - GrtQ and Unitrivalent Graphs

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Explore rational homotopy of embedding spaces, focusing on grtQ and unitrivalent graphs in this advanced mathematical lecture.
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1 Lesons
40 minutes
On-Demand
Free-Video
Renzo Ricca

From Linking Numbers to Vortex Motion and Torus Knots - Lecture 3

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Explore advanced concepts in topological vortex dynamics, linking numbers, vortex motion, and torus knots in this comprehensive scientific lecture.
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1 Lesons
1 hour 50 minutes
On-Demand
Free-Video
Renzo Ricca

On Quantum Vortex Knots and Links

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Explore quantum vortex knots and links in this advanced seminar, delving into cutting-edge research on quantum topology and its applications.
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1 Lesons
53 minutes
On-Demand
Free-Video
Renzo Ricca

The Beautiful Interplay of Topology and Physics

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Explore the fascinating connection between topology and physics, uncovering how mathematical concepts shape our understanding of the physical world.
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1 Lesons
44 minutes
On-Demand
Free-Video
Institut Henri Poincaré

Khovanov Homology and the Cinquefoil

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Explore Khovanov homology's detection of the (2,5) torus knot through advanced Floer homology and recent developments in knot theory.
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1 Lesons
59 minutes
On-Demand
Free-Video
Institut Henri Poincaré

Legendrian Torus and Cable Links

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Explore Legendrian torus and cable links, their classification, restrictions, and symmetries using convex surface theory applications.
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1 Lesons
49 minutes
On-Demand
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
On-Demand
Free-Video
NCCR SwissMAP

Poincaré Series and Linking of Legendrian Knots

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Explore analytic techniques in dynamics and geometry, focusing on Poincaré series and linking of Legendrian knots with G. Rivière.
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1 Lesons
59 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Gauss Realisability Conditions - From Error Correction to Formalization

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Explore Gauss Realisability conditions, their applications in error correction, and the journey towards formalization in mathematics, offering insights into advanced mathematical concepts.
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1 Lesons
45 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Prime, Knots and the Adele Class Space

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Explore geometric connections between primes and knots through scaling site theory, adele class space, and finite abelian extensions of Q, revealing insights into number theory and topology.
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1 Lesons
1 hour 14 minutes
On-Demand
Free-Video
Banach Center

Knots, Operator Algebras, and Physics - Part I

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Explore connections between knot theory, operator algebras, and physics, focusing on isotope links, transport numbers, and link diagrams.
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8 Lesons
2 hours 9 minutes
On-Demand
Free-Video
Banach Center

Link Homology and How to Compute It - Part 2

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Explore advanced techniques for computing link homology, building on foundational concepts to deepen understanding of topological invariants in knot theory.
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1 Lesons
51 minutes
On-Demand
Free-Video
Banach Center

Link Homology and How to Compute It - Part 1

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Explore link homology computation techniques and foundational concepts in this comprehensive mathematical lecture by Matt Hogancamp from Northeastern University.
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1 Lesons
48 minutes
On-Demand
Free-Video
Banach Center

Knot Quantum Invariants, Graphs, and Combinatorics - Part 3

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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
53 minutes
On-Demand
Free-Video
Banach Center

Link Homology and How to Compute It - Part 4

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Explore advanced concepts in link homology computation, focusing on cutting-edge techniques and theoretical foundations presented by Matt Hogancamp from Northeastern University.
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1 Lesons
49 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

Knot Quantum Invariants, Graphs, and Combinatorics - Part 1

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Explore quantum knot invariants, their connections to graph theory, and combinatorial applications in this advanced mathematical lecture.
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1 Lesons
56 minutes
On-Demand
Free-Video
Banach Center

Categorification of Quantum Invariants: From Knots to 3-Manifolds - Part 1

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Explore categorification of quantum invariants, focusing on knots and 3-manifolds. Delve into advanced mathematical concepts with expert Sergei Gukov from Caltech and Dublin IAS.
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1 Lesons
50 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
On-Demand
Free-Video
Banach Center

Detecting Positivity from Link Homology

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Explore Khovanov homology's applications in detecting link positivity and its extension to fibered positive links and L-space knots.
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1 Lesons
58 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
Banach Center

On the Structure of Skein Modules

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Explore Kauffman bracket skein modules, examining conjectures and theorems. Discover counterexamples and new insights into the structure of these modules in 3-manifolds.
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1 Lesons
54 minutes
On-Demand
Free-Video
Banach Center

Bordered Floer Theory, Hochschild Homology, and Links in S^1 × S^2

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Explore spectral sequences linking Khovanov homology to Heegaard Floer homology and their analogues for links in S^1×S^2, involving bordered Floer theory and Hochschild homology.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Banach Center

Algebras for Knots and Their Connections to Quiver Yangians

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Explore quiver Yangian algebras, their representations, and connections to knots through the knot-quiver correspondence and gluing construction.
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1 Lesons
56 minutes
On-Demand
Free-Video
Banach Center

How Many Quivers Does a Knot Have? - Knots-Quivers Correspondence and Symmetries

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Explore knots-quivers correspondence, equivalent quivers classification, and implications for symmetric quiver invariants in knot theory.
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1 Lesons
45 minutes
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Free-Video
Banach Center

Quiver Structures of Knot Invariants, Open Strings, and Recursion

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Explore quiver structures in knot theory, connecting HOMFLY-PT polynomials to motivic Donaldson-Thomas invariants through string theory and M-brane interactions.
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1 Lesons
1 hour 4 minutes
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Free-Video
Banach Center

Z-Disks in CP^2 - Enumeration and Boundary Knot Analysis

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Explore locally flat Z-disks in CP^2, focusing on enumeration and boundary conditions. Gain insights into topological isotopy and related smooth category problems.
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1 Lesons
59 minutes
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Free-Video
Centre de recherches mathématiques - CRM

Cluster Algebras and Hyperbolic Geometry

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Explore the application of cluster algebra to 2D and 3D hyperbolic geometry, examining ideal triangulations, Teichmuller spaces, and knot volumes through mutations and cluster variables.
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1 Lesons
1 hour 1 minute
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Free-Video
Centre de recherches mathématiques - CRM

Orderability of 3-Manifold Groups and the L-Space Conjecture

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Explore orderability of 3-manifold groups, focusing on the L-space conjecture and its connections to group orderability, taut foliations, and Heegaard Floer homology in hyperbolic 3-manifolds.
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1 Lesons
56 minutes
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Free-Video
Centre de recherches mathématiques - CRM

Left-Orderability and Toroidal 3-Manifolds

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Explore left-orderability in 3-manifolds with incompressible tori, using order-detection of slopes. Gain insights into the L-space conjecture through new evidence.
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1 Lesons
57 minutes
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Free-Video
Centre de recherches mathématiques - CRM

Non-standard Orders on Torus Bundles with One Boundary

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Explore non-standard bi-orderings of fundamental groups in torus bundles with one boundary, extending Perron-Rolfsen's work on standard orderings and Alexander polynomials.
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1 Lesons
49 minutes
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Free-Video