Hausdorff Center for Mathematics Courses

Comparing the Baum-Connes Conjecture and the Farrell-Jones Conjecture

Vergleich der Baum-Connes-Vermutung und der Farrell-Jones-Vermutung in der algebraischen und geometrischen Topologie, mit Fokus auf Gemeinsamkeiten und Unterschiede.

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

Spectral Truncations of Low-Dimensional Tori

Explore spectral truncations of low-dimensional tori, delving into advanced mathematical concepts and their applications in topology and geometry.

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

Rearrangement Lemma, Divided Differences & Multivariate Holomorphic Functional Calculus

Explore advanced mathematical concepts including rearrangement lemma, divided differences, and multivariate holomorphic functional calculus in this in-depth lecture.

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

Marie-France Vigneras - Representations of GLn(D) Near the Identity

Explore representations of general linear groups over p-adic fields, focusing on dimension formulas for fixed points under congruence subgroups and extensions to inner forms.

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

J. E. Rodriguez Camargo: A Local Jacquet-Langlands Correspondence for Locally Analytic D-Modules

Explore an equivalence between GL₂(F)-equivariant D-modules on Drinfeld space and D*^-equivariant D-modules on P¹, with applications to Scholze's functor and admissible representations.

• 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

Generic Character Sheaves for Parahoric Subgroups

Exploration of Lusztig's character sheaves theory, extending to positive-depth cases and addressing Lusztig's conjecture. Focuses on perverse sheaves and parahoric Deligne-Lusztig induction in representation theory.

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

Meromorphic Vector Bundles on the Fargues-Fontaine Curve

Explore meromorphic vector bundles on the Fargues-Fontaine curve and their role in connecting p-adic and perfect geometry approaches to the local Langlands correspondence conjecture.

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

Explicit Examples of Categorical Local Langlands

Explore explicit examples of categorical local Langlands, focusing on GL_2 and SL_2 groups, examining fully faithful functors, sheaf computations, and connections to Langlands classification.

• YouTube
• 1 hour 16 minutes
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

Alexander Petrov: On de Rham Cohomology in Positive Characteristic

Explores de Rham cohomology in positive characteristic, discussing Hodge decomposition analogs, isomorphism failures, and structures on de Rham complexes over F_p, including Sen operators and Frobenius pullback decompositions.

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

Categorical Local Langlands

Explore categorical local Langlands correspondence with Xinwen Zhu, delving into advanced mathematical concepts and their applications in number theory and representation theory.

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