Knot Theory Courses and Certifications

International Centre for Theoretical Sciences

Topological Strings, Knots, and Quivers - Lecture 1

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.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Harvard CMSA

Fibered Ribbon Knots vs. Major 4D Conjectures - Part 1

Delve into advanced mathematical concepts exploring fibered ribbon knots, their relationship to smooth 4D Poincaré conjecture, and criteria for extending fibrations in topological studies.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

ICTP Mathematics

Khovanov Homology and Strongly Invertible Knots

Explore Khovanov homology's applications to strongly invertible knots, uncovering new insights in knot theory and topology.

• YouTube
• 50 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

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
• On-Demand
• 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
• On-Demand
• Free Video

IMSA

Ribbon Concordances and Slice Obstructions: Experiments and Examples

Explore ribbon concordances between knots, computational methods, and results in low-dimensional topology. Joint work with Nathan Dunfield on slice obstructions and experimental approaches.

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

IMSA

Rational Slice Genus Bounds from Knot Floer Homology

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.

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

IMSA

Characterizing Slopes for Alternating Knots

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.

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

IMSA

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

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.

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

IMSA

Symmetric Unions and Ribbon Knots

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.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

IMSA

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

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.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

IMSA

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

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.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

IMSA

Braidings and Braid Equivalences

Explore braiding algorithms and braid equivalences for various knot types, including classical, virtual, and singular, with a focus on knotoids and braidoids.

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