Homological Algebra Courses and Certifications

Applied Algebraic Topology Network

Homological Algebra for Persistence Modules

Introduction to persistence modules in algebraic topology, exploring tensor products, Hom operations, and their role in homological algebra. Insights into preserving exact sequences and advanced concepts.

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

Applied Algebraic Topology Network

Real Multiparameter Persistent Homology

Explores real multiparameter persistent homology, addressing challenges and practical applications in data science. Introduces topological tameness and its implications for algebraic concepts and computational methods.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

The Module Structure of a Group Action on a Ring

Explore finite group actions on graded algebras, examining module multiplicities and their connections to homological algebra and geometric group actions.

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

ICTP Mathematics

Hochschild (co)homology and Geometric Regularity - Andrea Solotar

Explore Hochschild (co)homology's role in geometric regularity for associative algebras. Discover its applications in commutative and non-commutative settings, and its significance in algebraic geometry.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

The Snake Lemma and Indecomposable Chain Maps

Explore the snake lemma's connecting homomorphism through vector space chain complexes, using Escolar and Hiraoka's representation to simplify proofs and reveal key indecomposable chain maps.

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

Banach Center

Introduction to Koszul Duality - Part 5

Explore advanced concepts of Koszul duality, delving into its applications and theoretical foundations in algebraic topology and homological algebra.

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

Banach Center

Introduction to Koszul Duality - Part 4

Explore advanced concepts of Koszul duality, delving into its applications and theoretical foundations in algebraic topology and homological algebra.

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

Banach Center

Introduction to Koszul Duality - Part 3

Explore advanced concepts of Koszul duality, delving into its applications and theoretical foundations in algebraic topology and homological algebra.

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

Banach Center

Introduction to Koszul Duality - Part 2

Explore advanced concepts of Koszul duality, building on previous knowledge and delving into complex mathematical theories and applications.

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

Banach Center

Introduction to Koszul Duality - Part 1

Explore Koszul duality fundamentals with Vladimir Dotsenko, delving into algebraic structures and homological algebra concepts.

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

IIT Kanpur;  NPTEL

Category Theory

Explore foundational concepts in category theory, emphasizing extrinsic viewpoints and structural relationships. Gain insights applicable to mathematics, computer science, and theoretical physics.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

Chennai Mathematical Institute;  NPTEL

Computational Commutative Algebra

Explore computational commutative algebra using Macaulay2, covering topics from ideals to homological algebra, with emphasis on concrete calculations and applications to geometry.

• Swayam
• 12 weeks
• On-Demand
• Free Online Course

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

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

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