Hausdorff Center for Mathematics Courses

James Maynard: Half-Isolated Zeros and Zero-Density Estimates

Innovative method for detecting zeta function zeros, improving classical zero density results and providing insights into prime number distribution in short intervals.

• YouTube
• 1 hour 14 minutes
• Self-Paced
• Free Video

Blow-Up Solution for the Energy Critical Heat Equation

Explore classical and recent results on blow-up phenomena in critical Fujita equations, including infinite and finite-time blow-up, and learn about the inner-outer method and its applications.

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

Regularity of Free Boundaries in Obstacle Problems - Lecture IV

Explore advanced concepts in free boundary problems, focusing on regularity in obstacle problems. Learn key results, current research, and open challenges in this mathematical field.

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

A Supercritical Elliptic Equation in the Annulus

Explore advanced techniques for solving Sobolev-supercritical elliptic problems, focusing on symmetry and monotonicity properties to overcome compactness issues in mathematical analysis.

• YouTube
• 1 hour 50 minutes
• Self-Paced
• Free Video

Analysis of Nonlocal Conformal Invariant Variational Problems

Explore nonlocal conformal invariant variational problems, focusing on free-boundary minimal surfaces and integrability by compensation theory in 2D and nonlocal frameworks.

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

Blow Up Solution for the Energy Critical Heat Equation

Explore classical results and recent advancements in blow-up phenomena for critical Fujita equations, including infinite and finite-time blow-up, and the inner-outer method.

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

Fractional Convexity

Explores fractional convexity, extending Euclidean convexity to fractional settings. Examines fractional convex envelopes, their characterization as viscosity solutions, and connections to fractional Monge-Ampere equations.

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

Regularity of Free Boundaries in Obstacle Problems - Lecture II

Explore free boundary problems in PDE, focusing on regularity in obstacle problems. Learn key results, current research, and open questions in this mathematical field.

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

Blow Up Solution for the Energy Critical Heat Equation - Lecture II

Explore classical results and recent developments in blow-up phenomena for critical Fujita equations, including infinite and finite-time blow-up, and the inner-outer method.

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

Fourier Interpolation

Explore Fourier uniqueness and interpolation pairs, examining recent progress in explicit constructions and existence results for reconstructing functions from restricted data sets.

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

Traces of CM Values and Geodesic Cycle Integrals of Modular Functions

Explores generating series of CM value traces and geodesic cycle integrals of modular functions, covering theta lifts and applications to L-series and cycle integral rationality.

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

Blow Up Solution for the Energy Critical Heat Equation

Explore classical results and recent developments in blow-up phenomena for critical Fujita equations, including infinite and finite-time blow-up, using the inner-outer method.

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

The Polynomial Method for Point Counting and Exponential Sums - Lecture IV

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

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

The Restriction Problem and the Polynomial Method - Lecture IV

Explore Stein's restriction conjecture, Kakeya conjecture, and the polynomial method in restriction theory. Understand wave packet decomposition and intersection of tubes in hypersurfaces.

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

The Restriction Problem and the Polynomial Method - Lecture III

Explore Stein's restriction conjecture, Kakeya conjecture, and the polynomial method in restriction theory. Understand wave packet decomposition and intersection of tubes in hypersurfaces.

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