Algebraic Topology Courses and Certifications

Applied Algebraic Topology Network

Homotopy and Singular Homology Groups of Finite Digraphs

Explore advanced algebraic topology concepts through the computation of homotopy and singular homology groups in finite directed graphs, with applications in data analysis and network science.

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

Institute for Advanced Study

Introduction to Perverse Sheaves - Part 2

Delve into advanced mathematical concepts of perverse sheaves, exploring theoretical foundations and applications in topology and algebraic geometry through expert insights.

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

Applied Algebraic Topology Network

Sequential Topological Complexity of Group Homomorphisms

Delve into advanced algebraic topology concepts, exploring sequential topological complexity of maps and group homomorphisms through detailed mathematical analysis and computations.

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

Centre International de Rencontres Mathématiques

Cellular A1-Homology of Smooth Algebraic Varieties

Delve into cellular A1-homology theory for smooth algebraic varieties, exploring its computability, motivic analogues of Poincaré duality, and applications to smooth projective rational surfaces.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

IMSA

Characteristic Classes of Singular Spaces - Where We Are and Where Can We Go

Explore the evolution and future directions of characteristic classes in singular spaces, from historical developments to potential applications in mathematical research.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

IMSA

Thom Polynomials and Their Relationships to Characteristic Classes - An Exploratory Discussion

Explore the intricate relationships between Thom polynomials, characteristic classes, and their mathematical applications through an advanced theoretical discussion of quotient Chern classes.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Applied Algebraic Topology Network

Topological Complexity Seminar - Applied Algebraic Topology Network

Explore advanced mathematical concepts in topological complexity through expert seminars covering motion planning, manifold theory, and algebraic topology applications.

• YouTube
• 1 day 17 hours 29 minutes
• Self-Paced
• Free Video

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
• Self-Paced
• Free Video

Dr Trefor Bazett

Intro to the Fundamental Group - Algebraic Topology with Tom Rocks Maths

Explore algebraic topology and the fundamental group, from basic concepts to advanced applications like Brouwer's Fixed Point Theorem. Learn to analyze spaces through continuous deformations and group theory.

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

Fields Institute

Morse Complexity in Algebraic Topology

Explore advanced mathematical concepts in Morse theory and its computational complexity through expert analysis from the University of Chicago.

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

Applied Algebraic Topology Network

Spectral Relaxations of the Persistent Rank Invariant - Applied Algebraic Topology Network

Spectral relaxations of persistent rank invariant: A framework for continuous relaxations, offering stability and differentiability while preserving key properties and enabling efficient GPU-parallelized computation.

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

Churchill CompSci Talks

The Asynchronous Computability Theorem - Distributed Systems and Algebraic Topology

Explore the connection between distributed systems protocols and algebraic topology, proving consensus impossibility in asynchronous wait-free models through combinatorial structures.

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

Conference GSI

Avoiding the General Position Condition When Computing the Topology of a Real Algebraic Plane Curve

Explore advanced techniques for computing real algebraic plane curve topology without relying on general position assumptions. Gain insights into innovative mathematical approaches.

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

Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento (2023)

Explore homotopia, grupo fundamental e espaços de recobrimento através de exemplos práticos, teoremas clássicos e aplicações em topologia algébrica avançada.

• YouTube
• 1 day 22 hours 8 minutes
• Self-Paced
• Free Video

Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 06

Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental e espaços de recobrimento. Aprofunde-se em teoremas importantes e aplicações em superfícies compactas e espaços projetivos.

• YouTube
• 2 hours 24 minutes
• Self-Paced
• Free Video