Hausdorff Center for Mathematics Courses

Sharp Fourier Restriction Theory Over Finite Fields

Explore recent developments in sharp Fourier restriction theory over finite fields, examining the intersection of two key areas in mathematical research.

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

Inverse Results for Isoperimetric Inequalities - Part I

Explore inverse isoperimetric problems in graphs, focusing on the Fourier-Entropy-Influence conjecture and related inequalities. Discover applications to PAC learning and recent progress in the field.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Structure Theorems in Boolean Harmonic Analysis - Part I

Explore classical and modern structure theorems in Boolean Function Analysis, focusing on biased hypercube and symmetric group applications.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Signal Recovery, Restriction Theory, and Applications - Part I

Explores signal recovery in Fourier analysis, focusing on restriction theory and its applications to improve recovery conditions for missing frequencies in transmitted signals.

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

Numerical Simulation of Timoshenko-Beam Models for Fiber-Based Materials

Numerical simulation techniques for modeling fiber-based materials using Timoshenko beam models, focusing on efficient preconditioners and applications in paperboard mechanics.

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

Multiscale Finite Element Methods for Advection and Reaction-Diffusion Problems

Explore advanced finite element techniques for solving complex PDEs with oscillatory coefficients, focusing on multiscale methods for advection-diffusion and reaction-diffusion problems.

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

The Multiscale Hybrid Mixed Finite Element Method for Polygonal Meshes

Explores Multiscale Hybrid Mixed method for polygonal meshes, discussing upscaling, flux reconstruction, and a new variant with elliptic problems. Covers applications and collaborations in computational mathematics.

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

Log-Sobolev Inequalities for Matrix-Valued Functions

Explore advanced mathematical concepts of Log-Sobolev inequalities for matrix-valued functions, focusing on L1 variants and their applications in quantum systems and random matrices.

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

Random Graphs and Nonlinear Spectral Gaps

Explore discrete Poincaré inequalities in regular expander graphs, long-range expansion properties, and their implications for Banach space-valued functions, with improved estimates for Poincaré constants.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Approximate Polymorphisms in Boolean Functions

Explore approximate polymorphisms in theoretical computer science, focusing on stability results for functions satisfying certain properties and their implications.

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

Quantum Algorithms for Multiscale Partial Differential Equations

Explore quantum algorithms for multiscale PDEs, focusing on Schrödingerisation method and its quantum circuit implementation. Learn applications to linear multiscale PDEs and Hamilton-Jacobi equations.

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

Signal Recovery, Restriction Theory, and Applications - Lecture 3

Explore signal recovery techniques using Fourier transforms and restriction theory. Delve into improved recovery conditions and multi-linear approaches for multiple transmissions.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Structure Theorems in Boolean Harmonic Analysis - Lecture 4

Explore classical and modern structure theorems in Boolean Function Analysis, focusing on biased hypercube and symmetric group applications.

• YouTube
• 1 hour 12 minutes
• On-Demand
• Free Video

Functional Inequalities in Metric Geometry - Lecture 3

Explore discrete functional inequalities as invariants for bi-Lipschitz embeddings, examining nonlinear type/cotype, convexity, and spectral gap to deduce nonembeddability results for various graphs.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

On the Fourier Weight of F2 Polynomials

Explore Fourier weight of F2 polynomials, focusing on level k and degree d relationships. Gain insights into pseudorandom generators and recent mathematical proofs.

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