Knot Theory Courses and Certifications

Institut Henri Poincaré

Legendrian Torus and Cable Links

Explore Legendrian torus and cable links, their classification, restrictions, and symmetries using convex surface theory applications.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

NCCR SwissMAP

Categorified Traces and Colored SL_2 Knot Homology

Explore categorified traces and colored SL_2 knot homology in quantum topology, focusing on representation theory applications.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

NCCR SwissMAP

Poincaré Series and Linking of Legendrian Knots

Explore analytic techniques in dynamics and geometry, focusing on Poincaré series and linking of Legendrian knots with G. Rivière.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

BIMSA

Knot Invariants from Finite Dimensional Integration

Explore finite dimensional integration for computing powerful knot invariants, surpassing traditional methods in efficiency and rigor while challenging established notions in knot theory.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

Centre de recherches mathématiques - CRM

An Approach to Simon's Conjecture

Explore fundamental group epimorphisms between 3-manifolds and their implications for knot genera. Investigate conjectures related to Simon's conjecture in knot theory.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Renzo Ricca

On Quantum Vortex Knots and Links

Explore quantum vortex knots and links in this advanced seminar, delving into cutting-edge research on quantum topology and its applications.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

IMSA

Hans Boden, McMaster University - Virtual Knots and Algebraic Concordance

Explore virtual knots, concordance groups, and new invariants using mock Seifert matrices. Discover algebraic structures and open problems in knot theory.

• YouTube
• 1 hour
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

QuantumTopology

Khovanov Homology for Knots in Thickened Torus

Explore Khovanov homology for knots in thickened torus, delving into advanced topological concepts and their applications in quantum topology.

• YouTube
• 1 hour 35 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

From Hall Algebras to Legendrian Skein Algebras

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.

• YouTube
• 1 hour 1 minute
• Self-Paced
• Free Video

Dublin Institute for Advanced Studies DIAS

Learning 4-Dimensional Knot Invariants from the Jones Polynomial

Explore machine learning techniques in knot theory, focusing on learning 4D topological invariants from the Jones polynomial and their implications for understanding knot structures.

• YouTube
• 1 hour 48 minutes
• Self-Paced
• Free Video

Dublin Institute for Advanced Studies DIAS

Knots and Knotted Vortices

Explore the fascinating world of knots and knotted vortices in this engaging public lecture by Louis Kauffman, delving into their mathematical and physical properties.

• YouTube
• 1 hour 31 minutes
• Self-Paced
• Free Video

Applied Algebraic Topology Network

Hopf Arborescent Links, Minor Theory, and Decidability of the Genus Defect

Delve into advanced topological concepts exploring Hopf arborescent links, examining their four-dimensional properties and computational aspects of genus defects through minor theory and well-quasi-orders.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Banach Center

Knots and Categories

Explore connections between knot theory and category theory, delving into mathematical concepts and their interrelationships in topology and algebra.

• YouTube
• 1 hour 24 minutes
• Self-Paced
• Free Video