Homotopy Theory Courses and Certifications

International Centre for Theoretical Sciences

Introduction to Chromatic Homotopy Theory - Lecture 2

Explore chromatic homotopy theory's foundations, techniques, and applications in algebraic topology. Delve into advanced concepts and their significance in modern mathematical research.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

Global Noncommutative Geometry Seminar

Coarse Homotopy Theory and K-Theory

Explore coarse homotopy theory and K-theory with Ulrich Bunke, delving into advanced mathematical concepts in noncommutative geometry.

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

Hausdorff Center for Mathematics

What is Homotopy Type Theory - HoTT

Explore Homotopy Type Theory (HoTT) with Steve Awodey, delving into its foundations, applications, and significance in modern mathematics and computer science.

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

Fields Institute

Polyhedral Products in Motivic Homotopy Theory

Explore polyhedral products in motivic homotopy theory, delving into advanced mathematical concepts and their applications in algebraic topology and geometry.

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

International Centre for Theoretical Sciences

Introduction to Chromatic Homotopy Theory - Lecture 4

Explore chromatic homotopy theory's advanced concepts and applications in algebraic topology, building on previous lectures to deepen understanding of this complex mathematical field.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Introduction to Chromatic Homotopy Theory - Lecture 3

Explore chromatic homotopy theory's advanced concepts and applications in algebraic topology, building on previous lectures to deepen understanding of this complex mathematical field.

• YouTube
• 1 hour 27 minutes
• On-Demand
• Free Video

Simons Foundation

Prismatic Stable Homotopy Theory (March 14, 2025)

Explore trace methods in algebraic K-theory and their potential extension to other cohomological invariants in algebraic geometry with Jacob Lurie's analysis of prismatic stable homotopy theory.

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

Institut des Hautes Etudes Scientifiques (IHES)

Algebraic K-theory and Chromatic Homotopy Theory - Lecture 1

Delve into advanced mathematical concepts exploring the intersection of algebraic K-theory and chromatic homotopy theory, from spectra organization to Ravenel's conjectures and redshift phenomena.

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

Institut des Hautes Etudes Scientifiques (IHES)

Algebraic K-theory and Chromatic Homotopy Theory - Lecture 4

Delve into advanced mathematical concepts connecting algebraic K-theory with chromatic homotopy theory, exploring redshift phenomena and the resolution of the telescope conjecture through four comprehensive lectures.

• YouTube
• 2 hours 5 minutes
• On-Demand
• Free Video

Harvard CMSA

A Categorification of Quinn's Finite Total Homotopy TQFT with Application to TQFTs and Once-Extended TQFTs Derived from Discrete Higher Gauge Theory

Explore advanced categorification of Quinn's finite total homotopy TQFT, extending to once-extended versions using groupoids and linear profunctors for discrete higher gauge theory applications.

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

Institute for Advanced Study

Bounding Lagrangian Intersections Using Floer Homotopy Theory

Delve into advanced mathematical concepts exploring Lagrangian intersections through Floer homotopy theory, featuring new lower bound calculations and Steenrod squares applications in symplectic geometry.

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

IAS | PCMI Park City Mathematics Institute

Arithmetic Properties of Local Systems in Motivic Homotopy Theory

Delve into fundamental group theory and local systems in arithmetic geometry, exploring classical conjectures and recent developments in motivic representations and their arithmetic properties.

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

IAS | PCMI Park City Mathematics Institute

A^1-Algebraic Topology and Unstable Motivic Homotopy Theory - Part 2

Delve into unstable motivic homotopy theory, exploring Morel-Voevodsky spaces, homotopy sheaves, and fundamental theorems through expert guidance in advanced algebraic topology and geometry.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

IAS | PCMI Park City Mathematics Institute

A¹-Algebraic Topology and Introduction to Unstable Motivic Homotopy Theory - Part 1

Delve into unstable motivic homotopy theory, exploring Morel-Voevodsky spaces, homotopy sheaves, and motivic spheres through expert guidance in algebraic topology and geometry fundamentals.

• YouTube
• 1 hour 34 minutes
• On-Demand
• Free Video

IAS | PCMI Park City Mathematics Institute

A-Upper Motives in Motivic Homotopy Theory

Delve into advanced algebraic geometry concepts focusing on motivic structures of projective homogeneous varieties and reductive groups, featuring research by Karpenko, de Clercq, and Quéguiner-Mathieu.

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