Cohomology Courses and Certifications

International Mathematical Union

The Cohomology of Shimura Varieties with Torsion Coefficients and Applications

Explore Shimura varieties' cohomology with torsion coefficients and its applications in advanced mathematics, presented by Ana Caraiani.

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

Fields Institute

Cohomology of Stacks of Shtukas

Explore advanced algebraic geometry concepts, focusing on cohomology of shtuka stacks, with insights from Cong Xue's research in this specialized mathematical field.

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

IMSA

Top Weight Cohomology of M_g

Explore the top-graded weight filtration on open moduli spaces, with applications to exponential growth in H^{4g-6}(M_g, Q) dimensions, disproving previous conjectures.

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

IMSA

Cohomology Rings of Character Varieties

Explore cohomology rings of character varieties, including P=W conjecture proof and zero-dimensional COHA computation. Discover connections to Hilbert scheme of C^2 for punctured sphere case.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Plectic Cohomology of Mixed Shimura Varieties and Stacks

Explore joint work on plectic cohomology of mixed Shimura varieties and stacks with Tony Scholl from the University of Cambridge.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Fields Institute

Cohomology and Geometric Quantization of Toric Manifolds

Explore cohomology and geometric quantization in toric manifolds with expert Lisa Jeffrey, delving into advanced mathematical concepts and their applications in toric topology.

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

NCCR SwissMAP

Graph Complexes, GRT and Cohomology of GLn

Explore graph complexes, GRT, and GLn cohomology with Oxford's F. Brown. Delve into algebra, topology, and the Grothendieck-Teichmüller group in this advanced mathematical lecture.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

NCCR SwissMAP

Top Weight Cohomology of M_{g,n} and the Handlebody Group

Explore top weight cohomology of M_{g,n} and its connection to the handlebody group in algebraic topology and Grothendieck-Teichmüller theory.

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

Hausdorff Center for Mathematics

Using Currents to Represent Cohomology - Lightning Talk

Explore visual representations of cohomology and operations using currents, with special focus on geometric representations of Steenrod powers.

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

Institute for Advanced Study

Surprising Representations in Cohomology of Configurations in Graphs

Explore the fascinating representations in cohomology of graph configurations, their connection to braid arrangements, robotics, and moduli spaces of tropical curves, and the mysterious symmetric group representations in their cohomology.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Lie Algebroid Cohomology and Ideals in Lie Algebroids - Part 2

Delve into advanced concepts of Lie algebroid cohomology, focusing on Pontryagin characters of graded vector bundles and their role in representation theory and geometric reduction.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Lie Algebroid Cohomology and Ideals in Lie Algebroids - Part 1

Delve into advanced mathematical concepts of Lie algebroids, exploring cohomology, representations up to homotopy, and their homotopy invariance through expert analysis and theoretical frameworks.

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

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Lie Algebroid Cohomology and Ideals in Lie Algebroids - Part 3

Delve into advanced concepts of Lie algebroid ideals, geometric reduction techniques, and subrepresentations up to homotopy in this mathematical exploration of algebraic structures and their obstructions.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Institute for Advanced Study

A Derived Hecke Algebra in the Context of the Mod P Langlands Program - Rachel Ollivier

Explore derived Hecke algebras in mod p Langlands program, covering super singular modules, involution, trace maps, and twisted duals with Rachel Ollivier.

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

Hausdorff Center for Mathematics

Differential Topology for Diamonds

Explores Banach-Colmez tangent spaces for diamonds in smooth rigid analytic varieties, proposing conjectures on preperfectoid loci and cohomological smoothness, with examples and computations.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video