Hausdorff Center for Mathematics Courses

Helmut Abels - Diffuse and Sharp Interface Models for Two Phase Flows

Overview of analytic results for diffuse and sharp interface models in two-phase flow, discussing asymptotic limits as interfacial thickness approaches zero and exploring rigorous analytic results for sharp interface limits.

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

Non Uniqueness for the Transport Equation with Sobolev Vector Fields

Explore non-uniqueness in transport equations with Sobolev vector fields, challenging established theorems and offering new insights into solution behavior in mathematical physics.

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

Vorticity Measures and Vanishing Viscosity

Explore vorticity measures and vanishing viscosity in fluid dynamics, focusing on 2D Navier-Stokes equations and their relation to Euler equations in bounded domains.

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

Emil Wiedemann - On the Conservation of Energy-Entropy in Fluid Dynamics

Explores Onsager's Conjecture in fluid dynamics, covering energy conservation in Euler equations, compressible fluids, and entropy conservation, with applications to turbulence theory.

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

Derek Holt- Algorithms for Finitely Presented Groups III

Explore advanced algorithms for finitely presented groups, including Todd-Coxeter coset enumeration, Reidemeister-Schreier algorithm, and automatic structures. Learn applications in group theory and computational methods.

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

Neil Olver: On the Integrality Gap of the Prize Collecting Steiner Forest LP

Explores the integrality gap of the prize collecting Steiner forest LP, disproving the belief it was 2 and showing it's at least 9/4, with implications for approximation algorithms in combinatorial optimization.

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

Representation Theory for Groups of Lie Type I

Explore representation theory for finite groups of Lie type, covering structural properties, Harish-Chandra theory, and Deligne-Lusztig theory for classifying irreducible complex representations.

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

Matthias Mnich - Time- and Space-Optimal Algorithms for the Many-Visits TSP

Optimizing algorithms for the many-visits TSP problem, improving time and space complexity while maintaining logarithmic dependence on tour length. Discusses applications and compares with previous work.

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

Gomory Mixed Integer Cuts Are Optimal

Explores the theoretical superiority of Gomory mixed-integer cuts in integer programming, demonstrating their optimality in maximizing volume cut-off from the nonnegative orthant in infinite group relaxations.

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

Reinhard Kahle- How Computations Entered in Mathematical Foundations

Explore how computation became central to mathematical foundations, from Hilbert's Programme to the distinction between syntax and semantics in formalization and recursive theories.

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

Algorithms for Rank-1 Bimatrix Games

Explore algorithms for solving rank-1 bimatrix games efficiently, including polynomial-time methods for finding Nash equilibria and path-following techniques. Discusses complexity, uniqueness, and parameterized approaches.

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

Viswanath Nagarajan - Stochastic Load Balancing on Unrelated Machines

Explores stochastic load balancing on unrelated machines, presenting a constant factor approximation algorithm for minimizing expected makespan. Discusses LP relaxation and rounding techniques.

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

Hajime Ishihara - The Constructive Hahn Banach Theorem, Revisited

Explores constructive versions of the Hahn-Banach theorem, focusing on separation and extension theorems. Discusses geometric properties, subderivatives, and Gâteaux derivatives in functional analysis.

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

Robin Havea- On the Boundary of the Numerical Range

Explore challenges in constructive mathematics regarding the boundary and border of the numerical range, focusing on convexity analysis and its implications in various settings.

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

Hajime Ishihara- Constructive Reverse Mathematics- An Introduction and Recent Results

Explore constructive reverse mathematics, its foundations, and recent developments in classifying theorems across mathematical frameworks using logical principles and function existence axioms.

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