Hausdorff Center for Mathematics Courses

The P^1-Motivic Cycle Map

Explore P^1-motivic homotopy theory and its applications to various cohomology theories. Learn about the construction of the P^1-motivic cycle map and its implications for prismatic Poincaré duality.

• YouTube
• 58 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

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

Generalised Eigenvalues via Flach Classes

Explore the connection between generalized eigenvalues for mod p cusp forms and Galois cohomology classes, focusing on Flach's geometric construction and its implications for Hecke algebra actions.

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

On Symplectic Transformations of OG10-Type Hyperkähler Manifolds via Cubic Fourfolds

Explore symplectic birational transformations on OG10-type hyperkähler manifolds, focusing on LSV manifolds derived from cubic fourfolds and their cohomological actions.

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

The Defect of a Cubic Threefold

Explore geometric properties of singular cubic threefolds, relating defect to various characteristics. Insights from ongoing research with Lisa Marquand, inspired by Hyperkähler manifold construction.

• YouTube
• 31 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

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

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

The Monge-Ampere System - Convex Integration in Arbitrary Dimension and Codimension

Explore flexibility in weak solutions to the Monge-Ampere system via convex integration, covering isometric immersions and nonlinear elasticity with focus on Holder regularity in arbitrary dimensions.

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