Knot Theory Courses and Certifications

QuantumTopology

A. Akimova - Homologically Trivial Knots in Thickened Surfaces

Explore homologically trivial knots in thickened surfaces, examining their properties and implications for quantum topology research.

• YouTube
• 1 hour 31 minutes
• On-Demand
• Free Video

QuantumTopology

Conjugation of Global Knots

Explore the mathematical concept of conjugation in global knots, delving into advanced topological theories and their applications in quantum mechanics.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

QuantumTopology

A. Akimova - Homologically Trivial Knots

Explore homologically trivial knots in quantum topology, delving into advanced mathematical concepts and their implications for knot theory and related fields.

• YouTube
• 1 hour 23 minutes
• On-Demand
• Free Video

QuantumTopology

Connections of Knotoids and Knots in Thickened Torus

Explore connections between knotoids and knots in thickened torus, delving into advanced concepts in quantum topology and geometric knot theory.

• YouTube
• 1 hour 19 minutes
• On-Demand
• Free Video

QuantumTopology

HOMFLY Polynomial for Rational Knots

Explore the HOMFLY polynomial's application to rational knots, delving into advanced knot theory concepts and their mathematical implications.

• YouTube
• 1 hour 34 minutes
• On-Demand
• Free Video

QuantumTopology

Cocyclic Invariants of Knots

Explore cocyclic invariants of knots, delving into advanced mathematical concepts and their applications in quantum topology.

• YouTube
• 1 hour 30 minutes
• On-Demand
• Free Video

QuantumTopology

On the Number of Non Hyperbolic Knots

Explore the intriguing world of non-hyperbolic knots with Andrei Malyutin's in-depth analysis, offering insights into their quantity and mathematical properties.

• YouTube
• 46 minutes
• On-Demand
• Free Video

QuantumTopology

Matroids, Delta Matroids, and Knot Invariants

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.

• YouTube
• 56 minutes
• On-Demand
• Free Video

QuantumTopology

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

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.

• YouTube
• 59 minutes
• On-Demand
• Free Video

QuantumTopology

Y. Ilyina - Invariants of Knotoids

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

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

QuantumTopology

Ph. Korablev - Quantum Invariants of Knots

Explore quantum invariants of knots, delving into advanced mathematical concepts and their applications in topology and quantum mechanics.

• YouTube
• 1 hour 26 minutes
• On-Demand
• Free Video

QuantumTopology

A Normal Form for Highly Twisted Knots

Explore a novel normal form for highly twisted knots, delving into advanced concepts in quantum topology and knot theory.

• YouTube
• 52 minutes
• On-Demand
• Free Video

QuantumTopology

Classification of Prime Genus 1 Virtual Knots of Low Complexity

Explore prime genus 1 virtual knots of low complexity, their classification methods, and implications in quantum topology with A. Akimova's in-depth analysis.

• YouTube
• 51 minutes
• On-Demand
• Free Video

QuantumTopology

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

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.

• YouTube
• 1 hour 26 minutes
• On-Demand
• Free Video

QuantumTopology

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

Classification methods for prime virtual knots of genus 1, focusing on those with low complexity. Explores advanced concepts in knot theory and topology.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video