Homotopy Courses and Certifications

International Mathematical Union

Homotopy Patterns in Group Theory

Explore homotopy patterns in group theory, delving into advanced mathematical concepts and their applications in topology and algebra.

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

Applied Algebraic Topology Network

Two Methods of Efficiently Approximating Semi-Algebraic Sets Up to Homotopy

Explores efficient methods for approximating semi-algebraic sets, focusing on singly exponential complexity algorithms and their applications in algebraic geometry.

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

Applied Algebraic Topology Network

Computing Optimal Homotopies

Explore curve similarity measures and homotopy-based deformations in GIS, medical imaging, and graphics. Survey geometric and topological metrics, algorithms, and open questions in optimal homotopy computation.

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

Applied Algebraic Topology Network

Computing Optimal Homotopies

Explore optimal curve similarity measures using homotopy-based approaches, examining structural properties, algorithms, and open questions in topology and computational geometry.

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

Applied Algebraic Topology Network

Homology and Homotopy Properties of Scale-Free Networks

Delve into the mathematical study of scale-free networks through preferential attachment models, exploring how they influence higher-order connectivity, Betti number growth, and homotopy group properties in both finite and infinite graph settings.

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

Schmid College, Chapman University

What is Homotopy Type Theory (HoTT)?

Discover the historical, philosophical, and mathematical foundations of Homotopy Type Theory (HoTT), a revolutionary branch of logic developed over the past 15 years.

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

Numerical Methods Applied to Chemical Engineering

Explore advanced numerical methods for solving complex chemical engineering problems, including heat transfer, fluid mechanics, and molecular simulation. Gain practical skills in computational techniques.

• MIT OpenCourseWare
• On-Demand
• Free Online Course

Institute for Advanced Study

Lie Algebras and Homotopy Theory - Jacob Lurie

Explore connections between Lie algebras and homotopy theory, covering fundamental groups, Whitehead brackets, and Quillen's theorem in this advanced mathematics seminar.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Motivic, Equivariant and Non-commutative Homotopy Theory - Summer School 2020

Explore advanced topics in motivic, equivariant homotopy theory and non-commutative geometry through expert lectures covering latest developments in mathematical foundations and applications.

• YouTube
• 1 day 9 hours 42 minutes
• On-Demand
• Free Video

Harvard CMSA

Workshop on Quantum Field Theory and Topological Phases via Homotopy Theory and Operator Algebras

Explore advanced quantum field theory and topological phases through homotopy theory and operator algebras in this intensive workshop featuring leading experts from Harvard, Caltech, and more.

• YouTube
• 1 day 10 hours 3 minutes
• On-Demand
• Free Video

IAS | PCMI Park City Mathematics Institute

Motivic Homotopy Theory

Explore advanced mathematical concepts connecting algebraic geometry, topology, and arithmetic through motivic homotopy theory with leading experts in this specialized field.

• YouTube
• 1 day 23 hours 16 minutes
• On-Demand
• Free Video

International Mathematical Union

Stable Homotopy Groups of Spheres and Motivic Homotopy Theory

Survey of stable homotopy groups of spheres computation, covering classical methods, Mahowald's Uncertainty Principles, and new techniques using motivic homotopy theory. Includes recent computations and future research directions.

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

International Centre for Theoretical Sciences

Basic Homotopy Theory by Samik Basu

Explore fundamental concepts in homotopy theory, including maps, CW complexes, equivalences, and fibrations. Gain insights into key computations and sequences in this foundational area of topology.

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

Institut des Hautes Etudes Scientifiques (IHES)

Stable Homotopy Groups, Higher Algebra, and the Telescope Conjecture

Explore stable homotopy groups, spectra, and their applications in topology and geometry. Gain insights into fundamental concepts shaping modern algebraic topology and related fields.

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

Institut des Hautes Etudes Scientifiques (IHES)

Motivic Stable Homotopy Theory - Lecture 3

Explore advanced motivic stable homotopy theory, including P1-spectra, P-homotopy invariance, and applications to algebraic K-theory. Gain insights into non-A1-invariant theories and connections to p-adic cohomology.

• YouTube
• 1 hour 20 minutes
• On-Demand
• Free Video