Hausdorff Center for Mathematics Courses

Distinguishing Groups and the Group Isomorphism Problem

Explore the scale function in totally disconnected, locally compact groups, its computation methods, and the challenges in obtaining representations for certain groups. Insights into group theory and isomorphism problems.

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

Growth in Linear Algebraic Groups and Permutation Groups

Exploración de límites de diámetro en grupos simétricos y algebraicos lineales, con énfasis en técnicas simplificadas y conexiones entre diferentes enfoques matemáticos.

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

Stability and Invariant Random Subgroups I

Explore stability in permutation groups, unimodular random networks, and invariant random subgroups. Learn decision methods for equations in group theory and graph theory.

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

Derek Holt- Algorithms for Finitely Presented Groups I

Explore fundamental algorithms for computing in finitely presented groups, including Todd-Coxeter coset enumeration and Reidemeister-Schreier algorithm, with practical examples and applications.

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

Derek Holt- Algorithms for Finitely Presented Groups II

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

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

Beating the Integrality Ratio for S-T-Tours in Graphs

Explores a novel algorithm for the s-t-path graph TSP, achieving a 1.497 approximation ratio and surpassing the known integrality ratio of 3/2 through innovative techniques.

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

Computing with Gödel's Completeness Theorem

Explore computational approaches to Gödel's completeness theorem, including Krivine's "exploding models," A-translation, and Kripke forcing, with insights on reifying validity proofs into derivability proofs.

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

A 1.5-Approximation for Path TSP

Explores a 1.5-approximation algorithm for the Metric Path Traveling Salesman Problem, introducing novel techniques to handle larger s-t cuts and achieve a simplified approach matching Christofides' TSP algorithm.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Nucleolus of Cooperative Games

Explore fair profit distribution in cooperative games through the concept of nucleolus, focusing on weighted voting and matching games. Learn computational methods for this ancient fairness principle.

• YouTube
• 1 hour 3 minutes
• On-Demand
• Free Video

Erik Palmgren: From Type Theory to Setoids and Back

Exploring setoids in constructive mathematics, their implementation in proof assistants, and their role in formalizing Bishop-style mathematics and Martin-Löf type theory models.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Giovanni Sambin - Pointfree Topology Is Real and Pointwise Is Ideal

Explore dynamic perspectives in mathematics, blending computation and spatial intuition. Learn about positive topology, effective pointfree approaches, and the balance between real and ideal mathematical concepts.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Notions of Booleanization in Pointfree Topology

Explores overlap algebras as a potential solution to retain features of Boolean locales while recovering classical properties in intuitionistic pointfree topology.

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

Two Constructive Approaches to Probability Theory

Explores constructive approaches to probability theory, comparing frequentist and pointfree metric methods with classical Kolmogorov axioms and other paradigms in mathematics.

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

Iosif Petrakis - Bishop Spaces and the Problem of Constructivizing General Topology

Explores Bishop spaces as a constructive alternative to classical topology, overcoming obstacles in continuity and compactness. Presents key results and connections to other constructive space notions.

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

Algorithms for Computing Syzygies Over VX 1, …, X N, V a Valuation Ring

Explore algorithms for computing syzygies in polynomial rings over valuation domains, focusing on a general method without Gröbner bases and its combinatorial termination proof.

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