Knot Theory Courses and Certifications

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

Institute for Pure & Applied Mathematics (IPAM)

Using Machine Learning to Formulate Mathematical Conjectures - IPAM at UCLA

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.

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

QuantumTopology

On Knot Theoretical Counterpart of the Groups G^k_n

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.

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

QuantumTopology

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

Explore picture valued invariants, groups, and applications of virtual knot theory with Professor Vassily Manturov in this advanced mathematics lecture.

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

IMSA

Skein Exact Triangles in Equivariant Singular Instanton Theory

Explore knot signatures and singular instanton homology, focusing on skein exact triangles in equivariant theory. Uncover new insights into link invariants and their categorifications.

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

IMSA

Crossing Numbers of Whitehead Doubles

Explore the connection between colored Jones polynomials and crossing numbers of Whitehead doubles, revealing insights into satellite knots' minimum crossing numbers.

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

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

Galileo Galilei Institute

Introduction to BPS Spectra and Quantum Invariants - Lecture 2

Explore BPS spectra and quantum invariants in theoretical physics, delving into advanced mathematical concepts and their applications in modern quantum theory.

• YouTube
• 1 hour 32 minutes
• On-Demand
• Free Video

Galileo Galilei Institute

Introduction to BPS Spectra and Quantum Invariants - Lecture 3

Explore BPS spectra and quantum invariants in theoretical physics, delving into advanced mathematical concepts and their applications in modern quantum theory.

• YouTube
• 1 hour 45 minutes
• On-Demand
• Free Video

Galileo Galilei Institute

Exponential Networks and DT Invariants

Explore exponential networks and Donaldson-Thomas invariants in this advanced mathematics lecture, delving into complex algebraic structures and topological insights.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Galileo Galilei Institute

HOMFLYPT Skein Curve Counts and Recursions

Explore HOMFLYPT skein theory, curve counting, and recursive techniques in knot theory with insights from Tobias Ekholm's advanced mathematical lecture.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Galileo Galilei Institute

HOMFLYPT - Skein Curve Counts and Recursions

Explore advanced mathematical concepts in skein theory, focusing on curve counts and recursive techniques in topology and knot theory.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video