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Algebra
Homological Algebra

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Master chain complexes, persistence modules, and Koszul duality to solve problems in topology, algebra, and data analysis. Access specialized lectures from leading mathematics institutes on YouTube, covering applications from commutative algebra to persistent homology for advanced mathematical research.

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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
Fields Institute
Homological Algebra for Binary Forms

Explore homological algebra techniques for binary forms, examining their applications in commutative algebra and related mathematical structures.
- YouTube
- 46 minutes
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Fields Institute
A Duoidal Approach to Homological Algebra

Explore duoidal structures and their applications to homological algebra in this advanced mathematical presentation by Dai Tamaki from Shinshu University.
- YouTube
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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
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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
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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
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- 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.
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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.
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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.
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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.
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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.
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Banach Center
Introduction to Koszul Duality - Part 1

Explore Koszul duality fundamentals with Vladimir Dotsenko, delving into algebraic structures and homological algebra concepts.
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- 53 minutes
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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
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BIMSA
Complexes from Complexes

Explore advanced mathematical structures as Kaibo Hu examines how complex systems can be constructed from other complex systems in this specialized mathematics lecture.
- YouTube
- 1 hour 3 minutes
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BIMSA
Lattice Homology - The Unifying Construction

Explore lattice homology as a unifying mathematical construction in this advanced topology lecture by András Némethi at BIMSA's international conference.
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