Hausdorff Center for Mathematics Courses

The Restriction Problem and the Polynomial Method - Lecture I

Explore Stein's restriction conjecture, the Kakeya conjecture, and the polynomial method in harmonic analysis. Learn about wave packet decomposition and its applications in studying hypersurface-supported functions.

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

Marina Iliopoulou- Three Polynomial Methods for Point Counting, Lecture II

Explore three powerful polynomial methods for point counting: Dvir's Kakeya problem solution, Guth-Katz's polynomial partitioning, and the slice rank method for arithmetic progressions.

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

Marina Iliopoulou - Three Polynomial Methods for Point Counting, Lecture I

Explore three powerful polynomial techniques for point counting: Dvir's method, polynomial partitioning, and slice rank method, with applications in finite fields and geometry.

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

A Stationary Set Method for Estimating Oscillatory Integrals

Explore a stationary set method for estimating oscillatory integrals, with applications in number theory and Fourier analysis. Learn about o-minimal structures and geometric interpretations of upper bounds.

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

Ciprian Demeter - Restriction of Exponential Sums to Hypersurfaces

Explore exponential sums on hypersurfaces, focusing on sharp moment inequalities and scale-independent results. Gain insights into critical exponents and Hardy-Littlewood lemmas.

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

On Optimal Transport with Respect to Non-Traditional Costs

Explore optimal transport with non-traditional costs, focusing on c-transforms, c-subgradients, and conditions for Brenier-type maps. Includes examples like the polar cost in function polarity transforms.

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

Keith Ball- Restricted Invertibility

Explore restricted invertibility in mathematics, covering the Kadison-Singer problem and Bourgain-Tzafriri's argument, with insights on selection theorems and related concepts.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Non-Asymptotic Results for Singular Values of Gaussian Matrix Products

Explore non-asymptotic results for singular values of Gaussian matrix products, including convergence rates and Lyapunov exponent normality, based on joint research with Boris Hanin.

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

Vlad Yaskin- A Solution to the 5th and 8th Busemann-Petty Problems Near the Euclidean Ball

Explore solutions to complex geometric problems near the Euclidean ball, focusing on the 5th and 8th Busemann-Petty problems and their positive outcomes in specific conditions.

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

On Some Tight Convexity Inequalities for Symmetric Convex Sets

Explores tight convexity inequalities for symmetric convex sets, focusing on Gaussian measure, isoperimetric problems, and Dirichlet-Poincare inequality. Discusses progress using L2 methods and energy minimization.

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

Outliers in Sparse Wigner Matrices

Explore the impact of sparsity on extreme eigenvalues in Wigner matrices, including phase transitions and outlier emergence in the semi-circular law. Joint work with Konstantin Tikhomirov.

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

The Projective/Injective Ratio and GPTs

Explore tensor products in normed spaces, examining projective and injective norms' differences. Discover applications in physics, probabilistic theories, and XOR games, using geometry and random matrix techniques.

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

Recent Progress on the KLS Conjecture

Explore recent advancements in the KLS conjecture, its implications, and the stochastic localization technique used to achieve current best bounds for the Cheeger isoperimetric coefficient.

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

Emanuel Milman: Functional Inequalities on Sub-Riemannian Manifolds via QCD

Explores functional inequalities on sub-Riemannian manifolds using QCD, offering novel quantitative estimates for Poincaré and log-Sobolev inequalities with applications to Heisenberg groups.

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

Erik Broman- Higher Dimensional Stick Percolation

Explore higher dimensional stick percolation, its applications in physics and chemistry, and the scaling of critical parameters as stick length increases in arbitrary dimensions.

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