Hausdorff Center for Mathematics Courses

Dormancy Phenomena in Cancer Progression

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Explore dormancy mechanisms in cancer progression, their role in therapy resistance and metastasis, and mathematical models used to study these phenomena. Gain insights into open questions and potential research directions.

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

What Can Categorical Local Langlands Do for You?

Explore conjectures linking categorical and classical local Langlands correspondences, examining their relationships and current understanding in this advanced mathematics lecture.

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

Duality in P-adic Pro-etale Cohomology of Analytic Curves

Explore duality theorems in p-adic pro-etale cohomology of analytic curves, delving into advanced mathematical concepts and recent research findings in this specialized field.

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

The Finite Slope Part of Overconvergent Cohomology & Coherent Sheaves on Spaces of

Explores overconvergent cohomology, eigenvarieties, and coherent sheaves in p-adic automorphic forms. Discusses a conjecture on computing coherent sheaves using Galois representation stacks and its relation to p-adic Langlands program.

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

Tasho Kaletha- A Local Langlands Conjecture for Disconnected Groups

Explore the generalization of Langlands' conjectures to disconnected groups, examining new phenomena and potential applications to refined local Langlands correspondence for both connected and disconnected groups.

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

Tony Feng- A New Approach to Breuil-Mezard Cycles

Explore a novel local and group-theoretic approach to the Breuil-Mezard Conjecture, connecting it to quantum groups and homological mirror symmetry in algebraic number theory.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Gamma Factors for Mod Representations of Finite General Linear Groups

Explores construction of gamma factors for mod 𝓁 representations, proving a converse theorem. Discusses overcoming challenges and relates to recent work on local Langlands in families.

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

Lucas Mann- Representation Theory via 6-Functor Formalisms

Explore abstract 6-functor formalisms and their application to representation theory of locally profinite groups, shedding light on classical results and p-adic Lie group representations.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

The Weight Part of Serre's Conjecture and the Emerton-Gee Stack

Explore the Breuil-Mezard conjecture's impact on local deformation rings and its connection to Serre's conjecture, focusing on recent advancements in moduli stack theory and p-adic Galois representations.

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

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

The Eilenberg-Watts Theorem and Morita Theory for C*-Categories

Explore the Eilenberg-Watts theorem and Morita theory in the context of C*-categories, delving into advanced mathematical concepts and their applications in functional analysis.

• YouTube
• 27 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