Homological Algebra Courses and Certifications

International Mathematical Union

Homological Algebraic Geometry

Explore semiorthogonal decompositions in algebraic geometry, including their properties, geometric significance, and novel applications in categorical constructions and singularity resolutions.

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

Institut des Hautes Etudes Scientifiques (IHES)

Analytic Stacks - New Foundations for Analytic Geometry

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.

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

Institut des Hautes Etudes Scientifiques (IHES)

Analytic Stacks - Lecture 6

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.

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

Institut des Hautes Etudes Scientifiques (IHES)

Analytic Stacks - Lecture 5

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples with renowned mathematician Peter Scholze.

• YouTube
• 1 hour 46 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Twisted K-theory in Motivic Homotopy Theory

Explore algebraic K-theory of vector bundles twisted by Brauer class, its role in motivic homotopy theory, and a new approach to the motivic spectral sequence for twisted K-theory.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Localizing Invariants and Algebraic K-theory - Part 1

Explore localizing invariants in algebraic K-theory, from classical foundations to recent developments, with emphasis on descent properties and applications.

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

Fields Institute

Modern Algebraic Geometry

Dive into advanced algebraic geometry concepts through 36 comprehensive lectures from the Fields Institute's graduate-level program covering contemporary mathematical techniques.

• YouTube
• 1 day 7 hours 32 minutes
• Self-Paced
• Free Video

Fields Institute

Graduate Course on K-Theory and C*-Algebras

Master advanced mathematical concepts in K-Theory and C*-Algebras through comprehensive graduate-level lectures from the Fields Institute's operator algebras program.

• YouTube
• 1 day 5 hours 22 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Connections Between Representation Theory and Geometry - Winter School

Explore advanced connections between representation theory and geometry through A-infinity structures, Fukaya categories, and homological mirror symmetry techniques.

• YouTube
• 15 hours 27 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Categorification, Representation Theory and Symplectic Geometry

Explore advanced mathematical connections between categorification, representation theory, and symplectic geometry through expert lectures on Hilbert schemes, Fukaya categories, and KLR algebras.

• YouTube
• 15 hours 14 minutes
• Self-Paced
• Free Video

Topos Institute

Cohomological Aspects of Information

Explore the mathematical foundations of information cohomology, examining Shannon entropy, differential entropy, and categorical perspectives on information theory through a cohomological lens.

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

IAS | PCMI Park City Mathematics Institute

Heegaard Floer Homology

Dive into Heegaard Floer homology through comprehensive lectures covering fundamental concepts and advanced applications in low-dimensional topology and knot theory.

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

Institute for Advanced Study

Geometry of Matroids Workshop

Explore advanced geometric structures and tropical methods in matroid theory through expert lectures on delta-matroids, quiver representations, and moduli spaces.

• YouTube
• 15 hours 29 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Introduction to A-Infinity Structures - Bernhard Keller

Explore A-infinity algebras, modules, and derived categories. Learn about topological origins, minimal models, and twisted objects in this advanced mathematics lecture.

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

Fields Institute

The Close Relation Between K Theory and TC Theory

Explores the tight relationship between algebraic K-theory and topological cyclic homology for p-adically complete rings, discussing recent results and future challenges in non-commutative cases.

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