Ring Theory Courses and Certifications

International Centre for Theoretical Sciences

Structure of Group Rings and the Group of Units of Integral Group Rings - Lecture 1

Explores group rings, their structure, and units of integral group rings. Covers idempotents, invertible elements, augmentation mapping, and constructions of units including Bass and cyclotomic units.

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

Michael Penn

Abstract Algebra - More Ring Theory Examples

Explore advanced ring theory concepts, including ideals and homomorphisms in matrix and polynomial rings, with in-depth examples and proofs.

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

Michael Penn

Abstract Algebra - Properties and Examples of Ring Homomorphisms

Explore ring homomorphisms' properties and examples, including proofs and comparisons of isomorphic groups versus rings in abstract algebra.

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

Michael Penn

Abstract Algebra - Ring Homomorphisms

Explore ring homomorphisms in abstract algebra, including definitions, examples, and key properties like multiplicative behavior and kernels.

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

Michael Penn

Abstract Algebra - Units and Zero Divisors of a Ring

Explore units and zero divisors in Zn and 2x2 real matrices, classifying elements and proving key properties in abstract algebra.

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

Fields Institute

From Rings of Operators to Noncommutative Geometry - Lecture 1

Explore the evolution from rings of operators to noncommutative geometry with renowned mathematician Alain Connes in this insightful Fields Institute lecture.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Global Noncommutative Geometry Seminar

Graded and Filtered K-Theory for Leavitt Path Algebras

Explore graded and filtered K-theory applications to Leavitt path algebras in this advanced mathematical seminar by Huanhuan Li.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Around NIP Noetherian Domains

Explore NIP Noetherian domains in this advanced mathematical lecture, delving into complex algebraic concepts and their implications.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

Centre International de Rencontres Mathématiques

Rings of Siegel-Jacobi Forms of Bounded Relative Index Are Not Finitely Generated

Explore Siegel-Jacobi forms and their non-finitely generated rings of bounded relative index in this advanced mathematical presentation by Ana Botero.

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

Institut des Hautes Etudes Scientifiques (IHES)

A Homotopical Approach to Crystalline Cohomology

Explore a homotopical approach to crystalline cohomology, focusing on higher homotopies for canonical lifts and easier global definition through gluing.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Analytic Stacks: New Foundations for Analytic Geometry

Explore new foundations for analytic geometry, covering light condensed abelian groups, analytic rings, analytic stacks, and examples.

• YouTube
• 2 hours 10 minutes
• On-Demand
• Free Video

NCCR SwissMAP

On the Image of the Trivial Source Ring in the Ring of Virtual Characters of a Finite Group

Explore the ring of virtual characters in finite groups, focusing on the trivial source ring and its connections to modular representation theory.

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

BunG Seminar

Localizing Motives, Algebraic KK-Theory and Refined Negative Cyclic Homology

Delve into advanced algebraic geometry concepts exploring localizing motives, their rigidity properties, and applications in refined negative cyclic homology and topological cyclic homology.

• YouTube
• 2 hours 29 minutes
• On-Demand
• Free Video

BunG Seminar

The Moduli Stack of Displays - Introduction to Zink's Display Theory

Delve into advanced algebraic geometry concepts through Zink's display theory, exploring Dieudonne theory extensions and connections to Barsotti-Tate groups in characteristic p settings.

• YouTube
• 2 hours 4 minutes
• On-Demand
• Free Video

BunG Seminar

Algebraic D-Modules: A Basic Review - Talk 12

Dive into the fundamentals of algebraic D-modules through a comprehensive review based on J. Bernstein's notes, exploring key concepts and theoretical foundations.

• YouTube
• 1 hour 36 minutes
• On-Demand
• Free Video