Hausdorff Center for Mathematics Courses

Jonathan Hickman: The Helical Maximal Function

Explore the helical maximal function in R3, its Lp boundedness, and related Fourier analytic tools. Gain insights into space curves and geometric measure theory.

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

Regularity of Free Boundaries in Obstacle Problems Lecture I

Explore regularity of free boundaries in obstacle problems, covering key concepts, proofs, and current research in this mathematical field of PDE and Geometric Measure Theory.

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

Pointwise Ergodic Theorems for Bilinear Polynomial Averages

Explore advanced ergodic theory concepts, focusing on bilinear polynomial averages and their convergence. Gain insights into recent developments in Bergelson's conjecture and related mathematical proofs.

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

Valentin Blomer - The Polynomial Method for Point Counting and Exponential Sums, Lecture III

Explore advanced techniques for counting points on curves over finite fields and estimating exponential sums using auxiliary polynomials and character sums.

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

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