Hausdorff Center for Mathematics Courses

On LP-Relaxations for the Tree Augmentation Problem

Explore LP-relaxations for tree augmentation, including dual-fitting algorithms, shadow-minimal solutions, and blocking trees. Gain insights into improved approximation techniques for combinatorial optimization problems.

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

An O(1)-Approximation for Minimum Spanning Tree Interdiction

Explore an O(1)-approximation algorithm for minimum spanning tree interdiction, improving upon previous O(log(m)) solutions. Learn about network interdiction and its applications in infrastructure protection.

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

On Element Connectivity Preserving Graph Simplification

Explores element-connectivity in graph simplification, focusing on reduction techniques, algorithmic results, and applications in network design. Highlights open problems and submodularity properties for faster algorithms.

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

Real Reductive Groups, K-Theory and the Oka Principle

Explore real reductive groups, K-theory, and the Oka principle in this advanced mathematics lecture, delving into representation theory and complex analysis concepts.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Bott Periodicity and the "Periodic Table" of Topological Insulators and Superconductors

Explore Bott periodicity's surprising role in condensed matter physics, focusing on topological insulators and superconductors, and their organization into a periodic table-like structure.

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

Curvature of the Determinant Line Bundle for Noncommutative Tori

Explore differential geometry of curved noncommutative tori, including spectral invariants and curvature of determinant line bundle for Dirac operators on noncommutative two tori.

• YouTube
• 55 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