Hausdorff Center for Mathematics Courses

Introduction to Parameterized Algorithms, Lecture I

Gentle introduction to parameterized complexity, focusing on basic techniques like branching, color coding, and kernelization. Explores connections to linear programming and discrete optimization.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Some Recent Progress on the Bochner Riesz Problem

Explore recent advancements in the Bochner Riesz problem, a key topic in harmonic analysis and Fourier analysis, with insights from cutting-edge research.

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

Exponential Sums and Oscillatory Integral - A Unified Approach

Explore a unified approach to exponential sums and oscillatory integrals, delving into advanced mathematical concepts and techniques in this comprehensive lecture.

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

Relative Trace Formulas for GL - 2 - and Analytic Number Theory

Explore relative trace formulas for GL(2) and their applications in analytic number theory, delving into advanced mathematical concepts and techniques.

• YouTube
• 1 hour 7 minutes
• Self-Paced
• Free Video

The Ratios Conjecture Over Function Fields

Explore the Ratios Conjecture for quadratic L-functions over function fields, including upper bounds for negative moments and partial results for various L-function ratios.

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

A Formula for Sobolev Seminorms Involving Weak L^p

Explore a mathematical formula for Sobolev seminorms involving weak L^p spaces, presented by Po-Lam Yung from the Hausdorff Center for Mathematics.

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

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