Homological Algebra Courses and Certifications

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• 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
• 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

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
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

IMSA

Generation in Characteristic P

Explore techniques for constructing generators in derived categories in nonzero characteristic, including joint research findings on this advanced mathematical topic.

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

IMSA

Derived Categories and Motives of Moduli Spaces of Vector Bundles on Curves

Explore derived categories and motives of moduli spaces of vector bundles on curves, their relationships, and recent developments in algebraic geometry.

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

IMSA

Homotopy Theories of Coalgebras

Explore homotopy theories of simplicial coalgebras, extending algebraic models for p-adic homotopy theory to include fundamental groups. Discover key ideas and potential G-equivariant analogs.

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

International Centre for Theoretical Sciences

Duality and Stratification in Commutative Algebra by Srikanth B. Iyengar

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

• YouTube
• 1 hour 12 minutes
• Self-Paced
• Free Video

QuantumTopology

Knot Invariants Arising from Homological Operations on Khovanov Homology

Explore advanced knot theory through homological operations on Khovanov homology, uncovering new invariants and their applications in quantum topology.

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