Homological Algebra Courses and Certifications

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

ICTP Mathematics

50 Years of Mathematics - The Work of Melvin Hochster

Explore the profound impact of Melvin Hochster's contributions to mathematics over five decades, highlighting key breakthroughs and their significance in the field.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

ICTP Mathematics

Direct Summands of Regular Rings - Part 3

Explore advanced concepts in tight closure theory, focusing on direct summands of regular rings and their applications in algebraic geometry and commutative algebra.

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

ICTP Mathematics

Stable Pair Invariants and Derived Categories - Lecture 1

Explore stable pair invariants and derived categories in mathematics with expert Y. Toda in this comprehensive lecture from ICTP Mathematics.

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

International Centre for Theoretical Sciences

Ambidexterity I by Neil Strickland

Explore duality phenomena in algebraic topology, commutative algebra, and modular representation theory. Learn about derived categories, triangulated structures, and Grothendieck duality theory in this advanced mathematics lecture.

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

International Centre for Theoretical Sciences

Ambidexterity in Topology and Algebra - Lecture 2

Explore ambidexterity in topology and algebra, focusing on duality phenomena and classification problems in tensor-triangulated categories. Gain insights into advanced mathematical concepts and their applications.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Residues and Trace Maps in Grothendieck Duality - Lecture 3

Explores residues and trace maps in Grothendieck duality theory, advancing understanding of algebraic geometry and commutative algebra concepts for researchers and advanced students.

• YouTube
• 1 hour 29 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Gorenstein Duality in Topology - Lecture 3

Explore Gorenstein duality in topology, examining its connections to algebraic geometry and representation theory. Gain insights into advanced mathematical concepts and their applications.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Gorenstein Duality in Topology - Lecture 2

Explore Gorenstein duality in topology, connecting algebraic concepts to topological structures and generalizing Poincaré duality for manifolds in this advanced mathematical lecture.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

International Centre for Theoretical Sciences

Duality and Stratification in Commutative Algebra - Lecture 2

Explore duality and stratification in commutative algebra, focusing on derived categories, triangulated structures, and connections to algebraic topology and representation theory.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video