Cohomology Courses and Certifications

Hausdorff Center for Mathematics

Some Remarks on Prismatic Cohomology of Rigid Spaces

Explore advanced mathematical concepts with Peter Scholze as he delves into prismatic cohomology of rigid spaces, offering insights and observations on this complex topic.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Motivic Cohomology of Carlitz Twists and Its Relation to Zeta Values and Polylogarithms

Explores t-motivic cohomology in function fields, focusing on Carlitz twists and their connections to zeta values and polylogarithms, drawing parallels with classical motivic theory.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Some Remarks on Prismatic Cohomology of Rigid Spaces

Explore advanced mathematical concepts with renowned mathematician Peter Scholze as he delves into prismatic cohomology of rigid spaces in this insightful lecture.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

Duality in P-adic Pro-etale Cohomology of Analytic Curves

Explore duality theorems in p-adic pro-etale cohomology of analytic curves, delving into advanced mathematical concepts and recent research findings in this specialized field.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Hausdorff Center for Mathematics

The Finite Slope Part of Overconvergent Cohomology & Coherent Sheaves on Spaces of

Explores overconvergent cohomology, eigenvarieties, and coherent sheaves in p-adic automorphic forms. Discusses a conjecture on computing coherent sheaves using Galois representation stacks and its relation to p-adic Langlands program.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

IMSA

Cohomology of Hurwitz Spaces

Explore the cohomology of Hurwitz spaces, focusing on branched covers of the affine line and their connections to braided Hopf algebras and a new family of braided operads.

• YouTube
• 1 hour
• Self-Paced
• Free Video

IMSA

Classifying Crystalline Interacting Topological Phases Through Equivariant Cohomology

Explore the classification of crystalline interacting topological phases using equivariant cohomology, examining assumptions and comparing with existing literature proposals.

• YouTube
• 55 minutes
• Self-Paced
• Free Video

Fields Institute

The Period-Index Problem for Higher Degree Galois Cohomology Groups Over Hensel Semi-Global Fields

Delve into advanced Galois cohomology theory, exploring period-index relationships over Hensel semi-global fields and their implications for higher degree groups.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Applied l-adic Cohomology I - Lecture 4

Delve into advanced analytic number theory concepts, exploring trace functions, l-adic cohomology, and their applications in modern mathematics through expert insights from Philippe Michel.

• YouTube
• 2 hours 14 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Applied l-adic Cohomology I - Lecture 3

Delve into advanced number theory concepts, exploring l-adic cohomology and trace functions through examples from modern analytic theory, with insights from Gauss, Weil, and Grothendieck's foundational work.

• YouTube
• 1 hour 51 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

Plumber's Algebra Structure on Symplectic Cohomology

Delve into advanced symplectic geometry concepts, exploring Plumber's PROP structures, nodal Riemann surfaces, and their applications to cohomological field theories and curve counting methods.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Prismatic Cohomology Relative Delta-Rings

Explore prismatic cohomology's evolution, comparing absolute and relative variants, and delve into a new generalization bridging the two approaches.

• YouTube
• 1 hour 17 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Motivic Cohomology of Schemes - Lecture 3

Explore advanced motivic cohomology theory for equicharacteristic schemes, covering cdh topology, K-theory filtration, and applications to algebraic geometry and zero cycles.

• YouTube
• 1 hour 28 minutes
• Self-Paced
• 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
• Self-Paced
• Free Video

Centre International de Rencontres Mathématiques

Prismatic and Syntomic Cohomology of Ring Spectra

Explore prismatic and syntomic cohomology of ring spectra, covering definitions, examples, theorems, and applications in chromatic homotopy and K-theory.

• YouTube
• 52 minutes
• Self-Paced
• Free Video