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Mathematics
Knot Theory

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Explore the fascinating world of knot theory, from basic knot invariants to advanced applications in topology, AI, and data analysis. Learn foundational concepts and visualization techniques through engaging YouTube lectures from leading mathematicians and institutions. Ideal for beginners interested in mathematics, computer science, or theoretical physics.

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IAS | PCMI Park City Mathematics Institute
Introduction to Knot Theory

Explore the mathematical foundations of knot theory through comprehensive lectures covering fundamental concepts, invariants, and applications in this advanced mathematics series.
- YouTube
- 6 hours 11 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
BIMSA
Polynomial Bounds on Reidemeister Moves in Knot Theory

Explore polynomial bounds on Reidemeister moves in knot theory, examining algorithms for trivial knot recognition and the relationship between diagram complexity and move sequences.
- YouTube
- 50 minutes
- On-Demand
- Free Video
IMSA
Knot Theory in Mathematics and AI Applications

Explore the fascinating world of knot theory and its connections to mathematics and AI in this engaging talk by Ernesto Lupercio from CINVESTAV.
- YouTube
- 1 hour 2 minutes
- On-Demand
- Free Video
Applied Algebraic Topology Network
Polytopal Crystallographic Sphere Packings for Geometric Knot Theory and Fractal Modeling

Explore polytopal crystallographic sphere packings and their applications in geometric knot theory and fractal modeling with customizable lacunar polygons.
- YouTube
- 45 minutes
- On-Demand
- Free Video
BIMSA
A Quick Trip to Knot Theory and Knot Data Analysis

Explore knot theory and its applications in data analysis with Professor Fengchun Lei, covering 3-manifold topology and topological data analysis concepts in this BIMSA Member Seminar.
- YouTube
- 47 minutes
- On-Demand
- Free Video
Harvard CMSA
Introduction to Knot Theory - September 23, 2024

Dive into the fascinating world of knot theory and its mathematical foundations, exploring topological concepts and their applications in modern mathematical analysis.
- YouTube
- 1 hour 27 minutes
- On-Demand
- Free Video
IAS | PCMI Park City Mathematics Institute
Twisted Topological Tangles - The Knot Theory of Knitting

Explore the fascinating intersection of mathematics and ancient knitting technology, discovering how 1D yarn creates complex 2D materials through topological principles and slip knot structures.
- YouTube
- 1 hour 1 minute
- On-Demand
- Free Video
Renzo Ricca
The Modern Legacy of Tait's Knot Theory

Explore how Tait's pioneering 19th-century knot theory foundations continue to influence modern mathematical physics and topology research today.
- YouTube
- 57 minutes
- On-Demand
- Free Video
Knotty Problems - Marc Lackenby

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.
- YouTube
- 52 minutes
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Insights into Mathematics
Knots and Surfaces I - Algebraic Topology - NJ Wildberger

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.
- YouTube
- 52 minutes
- On-Demand
- Free Video
Numberphile
Mathematical Knot Surfaces and Their Properties

Explore the fascinating intersection of mathematics and crochet as experts Sophie Maclean and Ayliean MacDonald demonstrate how knot theory relates to surfaces and topology through hands-on examples.
- YouTube
- 12 minutes
- On-Demand
- Free Video
ICTP Mathematics
From Knots to Number Theory I

Explore connections between quantum knot invariants and number theory, covering hyperbolic topology, Kashaev invariant, and quantum modularity. No prior knowledge required.
- YouTube
- 1 hour 33 minutes
- On-Demand
- Free Video
ICTP Mathematics
Some Classical Invariants of Links and Their Higher-Dimensional Analogues

Explore geometric invariants of links and knots, including higher-dimensional analogues, with examples of non-trivial cases in ambient isotopy.
- YouTube
- 1 hour 2 minutes
- On-Demand
- Free Video
International Mathematical Union
The Beauty of Braids - From Knot Invariants to Higher Categories

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

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