Hausdorff Center for Mathematics Courses

Representations of P-Adic Groups and Hecke Algebras

Explore p-adic group representations and Hecke algebras, focusing on supercuspidal representations, Bernstein blocks, and their equivalence to depth-zero blocks through Hecke algebra isomorphisms.

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

One-Dimensional Mod P Quaternionic Representations

Explore mod p cohomology of Lubin-Tate and Drinfeld spaces, and Hecke eigenspaces in quaternionic Shimura curves, using recent advancements in functor formalism and finiteness results.

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

João Lourenço- Towards Bezrukavnikov via P-adic Central Sheaves

Explore advancements in algebraic geometry, focusing on Bezrukavnikov's equivalence and p-adic central sheaves in the Witt vector affine flag variety, building on Kazhdan-Lusztig's work.

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

On Compactly Supported P-Adic Proétale Cohomology of Analytic Varieties

Explore p-adic proétale cohomology with compact support for analytic varieties, including properties, comparison theorems, and connections to de Rham cohomologies.

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

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
• Self-Paced
• Free Video

Marzieh Forough: Lifts of Completely Positive Maps

Explore the mathematical concept of lifts in completely positive maps, delving into advanced topics in quantum information theory and operator algebras.

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

Some Vanishing Results for Rational Completed Cohomology of Shimura Varieties

Explore p-adically completed cohomology in Shimura varieties, focusing on vanishing results for regular infinitesimal characters using Bhatt's Kodaira vanishing and translation functors.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Symmetric Power Functoriality for Hilbert Modular Forms

Explore symmetric power functoriality for Hilbert modular forms, comparing with elliptic modular cases in this advanced mathematics lecture by James Newton.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Geometric Eisenstein Series and Torsion Vanishing

Explores torsion vanishing in cohomology of Shimura varieties, combining geometric Eisenstein series, Fargues-Scholze local Langlands correspondence, and Hecke correspondences to extend previous results.

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

On Exotic Hecke Correspondences

Explores construction of exotic Hecke correspondences between mod p-fibers of different Shimura varieties, generalizing Xiao-Zhu's work and allowing non-isomorphic groups at p, leading to exotic Igusa variety isomorphisms.

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

Progress on Local Shtukas

Explore recent advancements in local shtukas, including joint research findings and their compatibility with global shtukas in characteristic p mathematics.

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

Srikanth Iyengar: Congruence Modules in Higher Codimensions

Explores advanced algebraic concepts, extending Wiles' and Diamond's work on congruence modules to higher dimensions, with applications to Hecke algebras and Shimura curves.

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

An Introduction to Geometric Sen Theory

Explore geometric Sen theory, its applications to Shimura varieties, and connections with proétale cohomology. Learn about solid locally analytic representations and perfectoid Shimura varieties.

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

Anticyclotomic P-adic L-functions for Rankin-Selberg Motives

Explore anticyclotomic p-adic L-functions for Rankin-Selberg motives, their construction, conjectures, and progress towards the Iwasawa main conjecture in this advanced mathematics lecture.

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

Cohomology Sheaves of Stacks of Shtukas

Explore cohomology sheaves of shtuka stacks, examining smoothness outside the level and analyzing level-specific phenomena in this advanced mathematical discussion.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video