Hausdorff Center for Mathematics Courses

Algebraic Perspectives of Persistence

Explore algebraic approaches to persistent homology, focusing on the stability of persistence diagrams and their relation to input data changes in topological data analysis.

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

Descriptive Geometry of Function Spaces

Explore the intricate world of function spaces and their descriptive geometry in this advanced mathematical lecture by Shmuel Weinberger, part of the Hausdorff Trimester Program.

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

Topological and Combinatorial Models of Directed Path Spaces

Explore topological and combinatorial models for directed path spaces in concurrency theory, focusing on methods to analyze execution paths and state spaces in computer science.

• YouTube
• 1 hour 25 minutes
• On-Demand
• Free Video

Hodge Theory for the Conservativity Conjecture

Explore Hodge theory's application to the conservativity conjecture in algebraic geometry and number theory with Joseph Ayoub's insightful lecture.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

Gonçalo Tabuada: Additive invariants of orbifolds

Explore additive invariants of orbifolds in algebraic geometry and number theory with Gonçalo Tabuada's insightful lecture from the Hausdorff Trimester Program workshop.

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

Novel Computational Perspectives of Persistence

Explore innovative computational approaches to persistence in algebraic topology, focusing on advanced techniques and their applications in data analysis and topological research.

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

Natural Homology Computability and Eilenberg Steenrod Axioms

Explore natural homology computability and Eilenberg Steenrod axioms in this advanced mathematics lecture, delving into applied and computational algebraic topology concepts.

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

Directed Paths on Cubical Complexes

Explore directed paths on cubical complexes in this advanced mathematics lecture, part of the Hausdorff Trimester Program on Applied and Computational Algebraic Topology.

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

Poisson U Statistics Subgraph and Component Counts in Random Geometric Graphs

Explore Poisson U statistics, subgraph counts, and component analysis in random geometric graphs, advancing knowledge in applied algebraic topology.

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

Mesoscale Crystal Plasticity Based on Continuum Dislocation Dynamics

Explores mesoscale crystal plasticity using continuum dislocation dynamics, presenting a novel mathematical model and numerical solution for predicting dislocation patterns in metal crystals.

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

Two-Scale FEMs for Non-Variational Elliptic PDEs

Explore advanced finite element methods for non-variational elliptic PDEs, focusing on two-scale approaches, monotonicity enforcement, and novel error estimation techniques for complex mathematical problems.

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

Fluctuations in Stochastic Homogenization

Explore fluctuations in stochastic homogenization, focusing on the homogenization commutator and its role in driving path-wise fluctuations of key quantities in the field.

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

A Family of Crouzeix-Raviart Non-Conforming Finite Elements in Two- and Three Spatial Dimensions

Explore non-conforming finite elements in 2D and 3D, focusing on Crouzeix-Raviart type. Learn about optimal a priori estimates, jump conditions, and explicit representations of local basis functions.

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

Homogenization Methods for Weakly Compressible Elastic Materials Forward and...

Explore homogenization methods for weakly compressible elastic materials, focusing on modeling, effective elasticity tensors, and estimating tissue porosity using mechanical responses.

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

Nonlocal Theories for Free Crack Propagation in Brittle Materials - Lecture 2

Explores mathematical upscaling of nonlocal fracture models, focusing on weak convergence, compactness, and Gamma-convergence for bridging mesoscopic and macroscopic scales in brittle material dynamics.

• YouTube
• 1 hour 25 minutes
• On-Demand
• Free Video