Commutative Algebra Courses and Certifications

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 Online Course

ICTP Mathematics

Gorenstein Property of Normalized Tangent Cones of Integrally Closed Ideals of 2-Dimensional Normal

Explore the Gorenstein property in normalized tangent cones of integrally closed ideals within 2-dimensional normal local rings, presented by K. Watanabe from Nihon University, Japan.

• YouTube
• 57 minutes
• On-Demand
• Free Online Course

Fields Institute

Recent Advances on Variants of the F-Signature

Explore recent developments in F-signature variants, focusing on mathematical advancements and their implications in algebraic geometry and commutative algebra.

• YouTube
• 54 minutes
• On-Demand
• Free Online Course

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
• On-Demand
• Free Online Course

NPTEL;  IISc Bangalore

Introduction to Algebraic Geometry and Commutative Algebra

Explore algebraic geometry and commutative algebra, covering topics from affine algebraic sets to integral extensions. Gain insights into key theorems and principles in this advanced mathematics course.

• YouTube
• 1 day 12 hours
• On-Demand
• Free Online Course

NPTEL;  IIT Bombay

Commutative Algebra

Comprehensive exploration of commutative algebra concepts through 60 lectures, covering fundamental principles and advanced topics for a deep understanding of algebraic structures.

• YouTube
• 1 day 5 hours
• On-Demand
• Free Online Course

NPTEL;  Chennai Mathematical Institute

Computational Commutative Algebra

This is an introductory course in computational commutative algebra. Topics in a typical first course in commutative algebra are developed along with computations in Macaulay2. The emphasis will be on concrete computations, more than on giving complete p…

• YouTube
• 1 day 7 hours
• On-Demand
• Free Online Course

Michael Penn

Abstract Algebra - Every PID is a UFD

Explore the connection between principal ideal domains and unique factorization domains, introducing key concepts like ascending chain condition and Noetherian rings.

• YouTube
• 26 minutes
• On-Demand
• Free Online Course

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 Online Course

International Centre for Theoretical Sciences

Stratification and Duality for Representations of Finite Groups - Lecture 2

Explore advanced concepts in finite group representation theory, focusing on stratification and duality principles. Gain insights into algebraic structures and their applications in mathematics.

• YouTube
• 1 hour 25 minutes
• On-Demand
• Free Online Course

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 Online Course

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 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 Online Course

International Centre for Theoretical Sciences

Stratification and Duality for Representations of Finite Groups - Lecture 4

Explore finite group representations through stratification and duality concepts. Delve into advanced algebraic techniques and their applications in modular representation theory.

• YouTube
• 1 hour 53 minutes
• On-Demand
• Free Online Course

International Centre for Theoretical Sciences

Residues and Trace Maps in Grothendieck Duality - Lecture 4

Explore residues and trace maps in Grothendieck Duality, advancing understanding of algebraic geometry and commutative algebra concepts within the broader context of dualities in topology and algebra.

• YouTube
• 1 hour 40 minutes
• On-Demand
• Free Online Course