Cohomology Courses and Certifications

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Cohomology of Arithmetic Groups and Integral Structures on Automorphic Representations

Explore cohomology of arithmetic groups and integral structures on automorphic forms, covering locally algebraic representations and their role in Langlands' philosophy.

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

IMSA

On the Nielsen Realization Problem and Cohomology of Mapping Class Groups of Non-orientable Surfaces

Exploración del problema de realización de Nielsen y cohomología de grupos de clases de mapeo en superficies no orientables, con aplicaciones en topología y teoría de grupos.

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

Institute for Advanced Study

Arithmetic Groups - Advanced Topics in Rigidity, Cohomology, and Dynamics

Explore advanced topics in arithmetic groups including rigidity theorems, congruence subgroups, bounded generation, and connections to dynamics and geometry.

• YouTube
• 1 day 54 minutes
• Self-Paced
• Free Video

Institute for Advanced Study

A Gentle Approach to Crystalline Cohomology - Jacob Lurie

Explore crystalline cohomology and the de Rham-Witt complex in algebraic geometry, with insights on alternative constructions and applications in positive characteristic fields.

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

Institute for Advanced Study

Floer Cohomology and Arc Spaces - Mark McLean

Explore Floer cohomology, arc spaces, and symplectic geometry with Mark McLean. Delve into contact structures, jet spaces, and mapping moduli spaces in this advanced mathematical lecture.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

International Mathematical Union

Hiroshi Iritani: On Decompositions of Quantum Cohomology D-Modules

Explore quantum cohomology D-modules and their decompositions with mathematician Hiroshi Iritani in this advanced mathematical lecture on complex algebraic geometry and topology.

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

Institut des Hautes Etudes Scientifiques (IHES)

Analytic Prismatization - Extending Prismatic Cohomology to Rigid-Analytic Spaces

Explore prismatic cohomology's extension to rigid-analytic spaces, including degeneration from analytic Hodge-Tate stack to Ogus-Vologodsky correspondence in characteristic p.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

De Rham Cohomology in Characteristic p - Advanced Topics

Explore advanced topics in de Rham cohomology of algebraic varieties in characteristic p, including stacky approaches and Steenrod operations' implications on spectral sequences.

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

Institut des Hautes Etudes Scientifiques (IHES)

Eigenvarieties and Completed Cohomology in p-adic Automorphic Forms

Explore connections between eigenvarieties and p-adic cohomology representation theory, focusing on p-adic families of finite slope automorphic eigenforms.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Prismatic Cohomology of Commutative Ring Spectra

Explore motivic filtrations on trace invariants of commutative ring spectra and their extension to prismatic cohomology, as presented by Arpon Raksit from MIT.

• YouTube
• 1 hour 9 minutes
• Self-Paced
• Free Video

M-Seminar, Kansas State University

BPS Cohomology and Quasi-BPS Categories - Lecture 4 of 4

Explore advanced BPS cohomology and quasi-BPS categories for symmetric stacks, focusing on quivers with potential and Higgs bundles on curves in algebraic geometry.

• YouTube
• 1 hour 19 minutes
• Self-Paced
• Free Video

M-Seminar, Kansas State University

BPS Cohomology and Quasi-BPS Categories - Lecture 3 of 4

Explore advanced algebraic geometry through BPS cohomology and quasi-BPS categories, focusing on symmetric stacks, quivers with potential, and Higgs bundles on curves.

• YouTube
• 1 hour 11 minutes
• Self-Paced
• Free Video

M-Seminar, Kansas State University

BPS Cohomology and Quasi-BPS Categories - Lecture 2 of 4

Explore BPS cohomology and quasi-BPS categories for symmetric stacks, focusing on quivers with potential and Higgs bundles, including Hall products and semiorthogonal decompositions.

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

M-Seminar, Kansas State University

BPS Cohomology and Quasi-BPS Categories - Lecture 1 of 4

Explore BPS cohomology and quasi-BPS categories for symmetric stacks, focusing on quivers with potential and Higgs bundles on curves through advanced algebraic geometry.

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

Institute for Advanced Study

p-Curvature and Non-Abelian Cohomology

Explore non-abelian cohomology structures for algebraic variety families and discover a new proof extending Katz's p-curvature conjecture to fundamental group representations.

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