Hausdorff Center for Mathematics Courses

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

Approximation Algorithms for Hard Augmentation Problems - Lecture III

Explore advanced network design techniques for increasing graph connectivity, focusing on recent approaches and advances in augmentation problems like Tree Augmentation and Connectivity Augmentation.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Aaron Sidford- Introduction to Interior Point Methods for Discrete Optimization, Lecture III

Explore interior point methods for discrete optimization, covering theory, advancements, and applications in maximum flow, bipartite matching, and linear programming.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Aaron Sidford: Introduction to Interior Point Methods for Discrete Optimization, Lecture II

Explore interior point methods for discrete optimization, covering theory, advances, and applications in flow, matching, and linear programming problems.

• YouTube
• 1 hour 18 minutes
• On-Demand
• Free Video

Tropical Solutions to Hard Problems in Auction Theory and Neural Networks - Lecture II

Explore tropical mathematics and its applications in neural networks, auction theory, and more, focusing on key ideas of tropical objects as limits and their polyhedral geometry.

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

Tropical Solutions to Hard Problems in Auction Theory and Neural Networks - Lecture I

Explore tropical mathematics and its applications in neural networks, auction theory, and more. Learn about min-plus algebra, tropical objects, and polyhedral geometry to solve complex problems.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Sums in Progressions to Squarefree Moduli Among Polynomials Over a Finite Field

Explore polynomial sums in progressions to squarefree moduli over finite fields, covering Fourier analysis, polynomial anatomy, and arithmetic functions.

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

Betsy Stovall- Fourier Restriction to the Sphere Is Extremizable More Often Than Not

Explore Fourier restriction to the sphere, focusing on extremizers and their prevalence. Delve into proofs, key limits, and spatial decomposition in this mathematical analysis.

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

Terence Tao- The Circle Method from the Perspective of Higher Order Fourier Analysis

Explore higher order Fourier analysis and its application to the circle method, offering new perspectives on multilinear averages and complex mathematical problems.

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

Terence Tao: Singmaster's Conjecture in the Interior of Pascal's Triangle

Explore Singmaster's conjecture in Pascal's triangle, combining Archimedean and non-Archimedean arguments to establish the conjecture in the triangle's interior region.

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

Large Sieve Inequalities for Families of Automorphic Forms

Explore advanced large sieve inequalities for automorphic forms, focusing on GL_3 spectral cases and recent progress in higher rank families. Gain insights into measuring family understanding.

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

Michael Christ- On Quadrilinear Implicitly Oscillatory Integrals

Explore advanced mathematical concepts in multilinear functionals, inequalities, and oscillatory integrals with a focus on quadrilinear forms and sublevel set inequalities.

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

Regularity of Free Boundaries in Obstacle Problems - Lecture III

Explore free boundary problems in PDE, focusing on regularity of solutions and interfaces. Learn about Stefan and obstacle problems, key results, and current research challenges.

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