Hausdorff Center for Mathematics Courses

Delocalization for Integer-Valued Height Functions in the Presence of Random Disorder

Explore delocalization properties of integer-valued Gaussian free fields with random disorder constraints through Bernoulli bond percolation on lattices.

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

A Block-Spin Renormalization on the Hierarchical Non-Linear Supersymmetric Hyperbolic Sigma Model

Explore block-spin renormalization techniques for hierarchical non-linear supersymmetric hyperbolic sigma models and their applications to quantum diffusion and stochastic processes.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Defining and Computing Characteristic Subgroups Without Automorphisms

Explore an innovative approach to defining characteristic subgroups through representation theory, bypassing circular dependence on automorphisms for certified computation.

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

Equations in Burnside Groups

Explore the rich structure of free Burnside groups B(r,n) and investigate when equation solutions in these groups originate from free group solutions.

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

The Tarski Problem for Hyperbolic Groups with Torsion

Explore the Tarski problem for hyperbolic groups with torsion, examining partial results and new difficulties caused by non-trivial finite order elements in group theory.

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

Towards the Construction of Multiple Massive SLE(2) Curves

Explore advanced mathematical construction of multiple massive SLE(2) curves through scaling limits of discrete processes, building on Makarov-Smirnov's near-critical models program.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

The Quantitative Geometry of Geodesics

Explore advanced geometric principles and theorems concerning geodesics, focusing on quantitative approaches to prove the existence and length bounds of these mathematical objects.

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

On the Equivalence of Distributional and Synthetic Ricci Curvature Lower Bounds

Explore the equivalence between distributional and synthetic approaches to defining lower Ricci curvature bounds on manifolds with continuous Riemannian metrics below C^2 regularity.

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

The Morse Landscape of the Lipschitz Functional

Explore the Morse landscape of the Lipschitz functional, examining how this height function behaves on maps between manifolds and investigating its peaks, valleys, and mountain passes through persistent homology.

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

Toward a Theory of Ricci Flow in Dimension 4

Explore the new compactness and partial regularity theory for Ricci flow in higher dimensions, focusing on dimension 4 and potential applications for surgery construction and singularity resolution.

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

The Willmore Energy Landscape of Immersed 2-Spheres - Lightning Talk

Explore the mathematical landscape of Willmore energy in relation to immersed 2-spheres in this concise lightning talk by Jona Seidel.

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

Assouad-Nagata Dimension: Distortion under Geometric Mappings in the Plane - Lightning Talk

Explore the concept of Assouad-Nagata dimension and how it changes under geometric mappings in the plane in this concise mathematical lightning talk.

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

Probabilistic Schwarzian Field Theory

Explore rigorous mathematical foundations of Schwarzian quantum field theory, including measure construction, partition functions, correlation calculations, and large deviation principles.

• YouTube
• 1 hour 7 minutes
• On-Demand
• Free Video

Towards Solvability of Toda Conformal Field Theories

Explore advanced mathematical physics through Toda Conformal Field Theories, their W-algebra symmetries, and connections to Gaussian Free Fields and representation theory.

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

The Functorial Formalism for Chiral 2D CFT - Definition and Methods for Constructing Examples

Explore the functorial approach to 2D conformal field theory, focusing on chiral CFT distinctions and construction methods for examples.

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