Hausdorff Center for Mathematics Courses

Harmonic Analysis Techniques for -Almost- Minimizers

Explore harmonic analysis techniques for (almost-)minimizers, focusing on free boundary theory and calculus of variations. Learn about applications to geometric measure theory and domain geometry.

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

Caleson Estimates on Solutions in Domains with Uniformly Rectifiable Boundaries

Explores elliptic operators and measures on domains with uniformly rectifiable boundaries, presenting estimates for elliptic measure and Green function associated with Dahlber-Kenig-Pipher operators.

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

Landscape Function and Its Relations With Eigenvectors of a Schrödinger Operator

Explore landscape functions and their connections to Schrodinger operator eigenvectors, covering effective potentials, energy computations, and exponential decay in various contexts.

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

Fast FPT-Approximation of Branchwidth

Explore efficient graph decomposition techniques and FPT algorithms for approximating branchwidth, with applications in structural graph theory and dynamic programming.

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

Pseudopolynomial-Time Algorithms for Optimization Problems

Explore fine-grained complexity theory and best-possible algorithms for discrete optimization problems, focusing on Subset Sum and related challenges in theoretical computer science.

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

Daniel Dadush- Integer Programming and the Kannan-Lovasz Conjecture

Explore advanced integer programming techniques, lattice theory, and the Kannan-Lovasz conjecture in this high-level overview of solving n-variable integer programs efficiently, with insights into recent progress and key concepts.

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

Breaching the 2-Approximation Barrier for Connectivity Augmentation

Explore connectivity augmentation, including incident links, Steiner tree reduction, and approximation algorithms. Learn about recent advances and open problems in this field.

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

Scheduling with Communication Delays via LP Hierarchies and Clustering

Explore advanced scheduling algorithms for jobs with precedence constraints and communication delays, focusing on LP hierarchies and clustering techniques for improved approximation ratios.

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

Francisco Criado - The Dual 1-Fair Packing Problem and Applications to Linear Programming

Explore proportional fairness in resource allocation, its dual problem, and applications to linear programming algorithms, focusing on geometric relationships and potential improvements.

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

Cynthia Vinzant - Log Concave Polynomials and Matroids

Explore strong log concavity in polynomials, its applications to matroids, and connections to combinatorics and geometry. Learn about recent developments and their implications.

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

Sparse Integer Programming Is FPT

Explore sparse integer programming's fixed-parameter tractability, its implications for parameterized complexity, and related concepts in variable dimension optimization.

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

Understanding and Extending the Quasipolynomial Time Algorithms for Parity Games

Explore quasipolynomial algorithms for parity games, universal trees, and their extensions to universal graphs. Discover recent advancements in game-solving algorithms and complexity bounds.

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

Face Structures of Tropical Polyhedra

Explore tropical polyhedra's face structures, focusing on monomial tropical polyhedra to overcome issues in classical definitions and investigate combinatorial properties.

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

Probabilistic Analysis of the Simpler Method and Polytope Diameter

Probabilistic analysis of simplex method and polytope diameter, exploring smoothed, well-conditioned, and random polytopes. Discusses improvements in complexity analysis and diameter bounds using shadow paths.

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

Tropical Solutions to Hard Problems in Auction Theory

Explore tropical mathematics' applications in auction theory, neural networks, and statistics through polytopes, algorithms, and semigroup matrices, unveiling powerful problem-solving techniques.

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