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

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

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

Topos Institute

Chain Complexes of Sets - Homology Made Simple

Discover a simplified approach to homological algebra through set-based chain complexes, making complex mathematical concepts more accessible without heavy algebraic prerequisites.

• YouTube
• 1 hour 4 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

Institute for Pure & Applied Mathematics (IPAM)

Classical Topology and Quantum Complexity - IPAM at UCLA

Explore the intersection of classical topology and quantum complexity, focusing on computational challenges in determining homology groups and their implications for quantum mechanics and data analysis.

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

Fields Institute

Applications of Topological Cyclic Homology in Algebraic K-Theory

Explore topological cyclic homology's applications in algebraic K-theory, covering key developments, impacts on number theory, and recent advancements in the field.

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