Hausdorff Center for Mathematics Courses

An Introduction to Auxiliary Polynomials in Transcendence Theory

Explore transcendence theory, focusing on Baker's Theorem and the structural rank conjecture. Learn complex analysis and commutative algebra techniques for proving key results in number theory.

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

The Orbit Method, Microlocal Analysis and Applications to L-Functions

Explore quantitative orbit method in microlocal analysis, its applications to representation theory, and implications for L-functions, including moment estimates and subconvex bounds.

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

New Avenues for the Circle Method - Lecture I

Explore adelic delta-method and nonabelian analogues in analytic number theory. Discover Poisson summation formulae for special varieties to generalize Fourier theory techniques.

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

Simon Myerson- Repulsion- A How-To Guide, Lecture III

Explore advanced techniques in polynomial analysis, focusing on repulsion methods to improve Birch's circle method for integral zeroes of multivariate polynomials.

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

Repulsion - A How-To Guide, Lecture I

Explore advanced techniques in polynomial analysis, focusing on repulsion methods to improve Birch's circle method for integral zeroes of multivariate polynomials.

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

Terence Tao - Pseudorandomness of the Liouville Function

Explore the Liouville pseudorandomness principle and its related conjectures, examining recent progress in understanding the statistical behavior of the Liouville function in number theory.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Sharp Examples for Decoupling and Related Questions

Explore open questions in decoupling, examining sharp examples and their connections to number theory and harmonic analysis. Gain insights into current challenges in the field.

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

Applications of Sharp Large Deviation Estimates in Asymptotic Convex Geometry

Explore sharp large deviation estimates in asymptotic convex geometry, including applications to random projections, norms, and volumes of Orlicz balls. Gain insights from recent research developments.

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

Some Comments on the Fundamental Gap of the Dirichlet Laplacian in Hyperbolic Space

Explore the fundamental gap of convex domains in hyperbolic space, comparing it with Euclidean space and examining different types of convexity in this advanced mathematical analysis.

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

Random Graph Matching with Improved Noise Robustness

Explores a new algorithm for exact matching of correlated Erdos-Renyi graphs, improving noise robustness in graph matching for applications in computer vision and biology.

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

On Bodies Floating in Equilibrium in Every Direction

Explore Ulam's Problem 19 on floating solids, examining historical and contemporary findings related to uniform density objects and their buoyancy properties.

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

One More Proof of the Alexandrov-Fenchel Inequality

Explore a concise proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies, presented by Bo'az Klartag in collaboration with other mathematicians.

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

Intrinsic Volumes on Pseudo-Riemannian Manifolds

Explore intrinsic volumes in pseudo-Riemannian geometry, covering Hadwiger's theorem, Weyl's principle, and Crofton formulas. Learn about recent developments in this advanced mathematical field.

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

Blaschke–Santaló Inequalities for Minkowski and Asplund Endomorphisms

Explores new isoperimetric inequalities for monotone Minkowski endomorphisms, extending to Asplund endomorphisms of log-concave functions, generalizing the Blaschke–Santaló inequality in convex geometric analysis.

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

On the Gaussian Minkowski Problem

Explore the Minkowski problem for Gaussian surface area measure, examining uniqueness and existence results in this collaborative research presentation.

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