Hausdorff Center for Mathematics Courses

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

Geometric Langlands over F_q

Explore strategies to deduce geometric Langlands conjecture for ℓ-adic sheaves, connecting F_q and complex number theories in advanced mathematics.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

P-adic Eichler-Shimura Theory and an Arithmetic Application

Explore p-adic Eichler-Shimura decomposition and its application to modularity, based on recent research in higher Coleman theory and completed cohomology.

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

On the Brumer-Stark Conjecture and Refinements

Explore recent advancements in the Brumer-Stark Conjecture, its connections to explicit class field theory, and the proof's completion, including implications for the Equivariant Tamagawa Number Conjecture.

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

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
• On-Demand
• Free Video

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
• On-Demand
• Free Video

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
• On-Demand
• Free Video