Hausdorff Center for Mathematics Courses

Finding Perfect Matchings in Bipartite Hypergraphs

Explore efficient algorithms for finding perfect matchings in bipartite hypergraphs, extending Haxell's condition and the Hungarian algorithm to hypergraph structures.

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

Panorama of Mathematics - Peter Scholze

Explore locally symmetric spaces and Galois representations with Peter Scholze, delving into hyperbolic 3-space, Bianchi manifolds, and non-abelian reciprocity laws in advanced mathematics.

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

Panorama of Mathematics - Laure Saint-Raymond

Explore particle dynamics, chaos theory, and statistical mechanics in large systems. Gain insights into ergodicity, entropy, and the Boltzmann equation with mathematician Laure Saint-Raymond.

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

Panorama of Mathematics - Darrell Duffie

Explore price transparency in over-the-counter financial markets, focusing on federal funds, contacting investors, uncertainty, and benchmark manipulation.

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

Panorama of Mathematics - Manjul Bhargava

Explore the Birch and Swinnerton-Dyer Conjecture with Fields Medalist Manjul Bhargava, delving into rational solutions of polynomial equations and the structure of points on cubic curves.

• YouTube
• 1 hour 16 minutes
• Self-Paced
• Free Video

Louis Theran: Rigidity of Random Graphs in Higher Dimensions

Explore rigidity properties of random graphs in higher dimensions and their connection to matrix completion, with insights on thresholds and optimal conditions.

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

Recent Results on Maximizing Submodular Functions

Explore recent advancements in submodular maximization, covering constrained and unconstrained scenarios for monotone and non-monotone functions within combinatorial optimization.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

Provable Submodular Function Minimization via Fujishige Wolfe Algorithm

Explore submodular function minimization through the Fujishige-Wolfe algorithm, analyzing its convergence and implications for combinatorial optimization.

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

The Power of Randomization - Distributed Submodular Maximization on Massive Datasets

Explore distributed algorithms for submodular maximization in machine learning, focusing on a parallel approach that achieves constant factor approximation guarantees for large-scale problems.

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

Randomized Composable Core-Sets for Submodular Maximization

Explores randomized composable core-sets for distributed submodular and diversity maximization, presenting improved algorithms and analysis techniques for big data optimization problems.

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

Maximizing Monotone Submodular Functions over the Integer Lattice

Explore advanced algorithms for maximizing monotone submodular functions on integer lattices, with applications in machine learning and combinatorial optimization.

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

Andreas E. Feldmann - A -embedding of Low Highway Dimension Graphs into Bounded Treewidth Graphs

Explores embedding low highway dimension graphs into bounded treewidth graphs, with applications in transportation network optimization problems like Travelling Salesman and Facility Location.

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

Ahmad Abdi- Packing Odd T-Joins With at Most Two Terminals

Explore graph theory with Ahmad Abdi as he delves into packing odd T-joins, covering applications, proof strategies, and open questions in combinatorial optimization.

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

Reassembling Trees for the Traveling Salesman

Explore advanced approximation algorithms for traveling salesman problems, focusing on tree reassembly techniques to improve solutions beyond traditional methods.

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

Zoltán Szigeti: On -2k,k--connected Graphs

Exploration of (2k,k)-connected graphs, focusing on orientation and construction methods. Covers arc-connectivity, vertex-connectivity, and splitting-off techniques for various graph structures.

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