Hausdorff Center for Mathematics Courses

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

On LP-Relaxations for the Tree Augmentation Problem

Explore LP-relaxations for tree augmentation, including dual-fitting algorithms, shadow-minimal solutions, and blocking trees. Gain insights into improved approximation techniques for combinatorial optimization problems.

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

An O(1)-Approximation for Minimum Spanning Tree Interdiction

Explore an O(1)-approximation algorithm for minimum spanning tree interdiction, improving upon previous O(log(m)) solutions. Learn about network interdiction and its applications in infrastructure protection.

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

On Element Connectivity Preserving Graph Simplification

Explores element-connectivity in graph simplification, focusing on reduction techniques, algorithmic results, and applications in network design. Highlights open problems and submodularity properties for faster algorithms.

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

Real Reductive Groups, K-Theory and the Oka Principle

Explore real reductive groups, K-theory, and the Oka principle in this advanced mathematics lecture, delving into representation theory and complex analysis concepts.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Bott Periodicity and the "Periodic Table" of Topological Insulators and Superconductors

Explore Bott periodicity's surprising role in condensed matter physics, focusing on topological insulators and superconductors, and their organization into a periodic table-like structure.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video

Curvature of the Determinant Line Bundle for Noncommutative Tori

Explore differential geometry of curved noncommutative tori, including spectral invariants and curvature of determinant line bundle for Dirac operators on noncommutative two tori.

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

Comparing the Baum-Connes Conjecture and the Farrell-Jones Conjecture

Vergleich der Baum-Connes-Vermutung und der Farrell-Jones-Vermutung in der algebraischen und geometrischen Topologie, mit Fokus auf Gemeinsamkeiten und Unterschiede.

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

Spectral Truncations of Low-Dimensional Tori

Explore spectral truncations of low-dimensional tori, delving into advanced mathematical concepts and their applications in topology and geometry.

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

Rearrangement Lemma, Divided Differences & Multivariate Holomorphic Functional Calculus

Explore advanced mathematical concepts including rearrangement lemma, divided differences, and multivariate holomorphic functional calculus in this in-depth lecture.

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

String Topology of Finite Groups of Lie Type

Explore string topology's role in understanding cohomology of finite Lie-type groups, connecting to loop spaces and algebraic geometry. Gain insights into recent developments in this mathematical field.

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

Jacob Lurie: A Riemann-Hilbert Correspondence in P-adic Geometry

Explore p-adic geometry and the Riemann-Hilbert correspondence, covering perfectoid spaces, crystals, and spectral methods in this advanced mathematics lecture.

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

The Module Structure of a Group Action on a Ring

Explore finite group actions on graded algebras, examining module multiplicities and their connections to homological algebra and geometric group actions.

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