Topological Spaces Courses and Certifications

Applied Algebraic Topology Network

Steve Scheirer - Relative Topological Complexity and Configuration Spaces

Explore relative topological complexity and configuration spaces in this advanced algebraic topology talk, covering definitions, results, and applications.

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

Applied Algebraic Topology Network

Bounds for the Higher Topological Complexity of Configuration Spaces

Explore bounds for higher topological complexities in unordered configuration spaces of trees and anchored configuration spaces of circles with two anchor points.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Sobolev Spaces in Extended Metric-Topological Measure Spaces

Explore Sobolev spaces in extended metric-topological measure spaces, focusing on Cheeger energy construction and properties in this general framework.

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

Global Noncommutative Geometry Seminar

Ample Groupoids, Topological Full Groups, Algebraic K-Theory Spectra and Infinite Loop Spaces

Explore ample groupoids, topological full groups, and their connections to algebraic K-theory spectra and infinite loop spaces in this advanced mathematics seminar.

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

Applied Algebraic Topology Network

Disk Configuration Spaces and Topological Complexity

Exploring disk configuration spaces, their topology, and topological complexity, focusing on ordered configurations of unit-diameter disks in infinite strips and their geometric implications.

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

Institute for Pure & Applied Mathematics (IPAM)

Topology of Moduli Spaces of Topological Theories and Applications to Codes

Explore moduli spaces of topological theories, their homotopy types, and applications to Hastings-Haah floquet codes in quantum error correction and quantum gravity.

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

IMSA

Classifying Spaces of Mapping Class Groups in Topological Surfaces

Explore the mathematical theory of mapping class groups, their role in topology and geometry, and recent developments in classifying spaces from Mexican mathematicians' research.

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

NPTEL;  IIT Bombay

An introduction to Point-Set-Topology Part-I

Comprehensive introduction to point-set topology, covering metric and topological spaces, continuity, compactness, and separation axioms. Ideal for students and professionals seeking a strong foundation in modern mathematics.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

ICTP Mathematics

Topology

Explore fundamental concepts in topology through comprehensive lectures covering topological spaces, continuity, compactness, and connectedness in this ICTP diploma series.

• YouTube
• 1 day 8 hours 2 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 2

Explore fundamental concepts of topology, including topological spaces, continuity, and homeomorphisms, with a focus on mathematical rigor and abstract reasoning.

• YouTube
• 1 hour 35 minutes
• On-Demand
• Free Video

ICTP Mathematics

Topology - Lecture 3

Explore fundamental concepts of topology, including continuous functions, homeomorphisms, and topological properties, in this advanced mathematics lecture.

• YouTube
• 1 hour 37 minutes
• On-Demand
• Free Video

Insights into Mathematics

Introduction to Homology in Algebraic Topology - Part 2

Explores cycles, boundaries, and homology in algebraic topology, focusing on graph modifications and using commutative group theory to analyze formal combinations of geometric elements.

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

Utrecht Geometry Centre

Introduction to Algebraic Topology

Discover fundamental concepts in algebraic topology including fundamental groups, van Kampen's theorem, and surface classification in this comprehensive introduction.

• YouTube
• 1 hour 36 minutes
• On-Demand
• Free Video

Algebraic Topology - Algebraic Invariants of Spaces

Explore algebraic invariants of topological spaces including fundamental groups, higher homotopy groups, homology, and cohomology with their homotopy invariance properties.

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

Michael Penn

A Complete Explanation of Hausdorff Spaces - Live Example

Discover the fundamental properties of Hausdorff spaces through clear explanations and practical examples in this concise topology lesson.

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