Hausdorff Center for Mathematics Courses

Constructive Mathematics - How to Not Believe in the Law of Excluded Middle

Explore constructive mathematics and challenge traditional logic with Andrej Bauer's thought-provoking examination of the Law of Excluded Middle in mathematical reasoning.

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

Mario Carneiro: System Introductions I - Lean

Explore the Lean theorem prover with Mario Carneiro in this introductory talk, covering its key features and applications in mathematical formalization.

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

What is Homotopy Type Theory - HoTT

Explore Homotopy Type Theory (HoTT) with Steve Awodey, delving into its foundations, applications, and significance in modern mathematics and computer science.

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

Mario Carneiro - Lessons from Metamath

Explore insights from Metamath, a formal proof verification system, and its implications for mathematical reasoning and proof automation.

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

Syntaxes for Binding and Their Semantics

Explore binding syntaxes and their semantics with Guillaume Allais, delving into advanced concepts in programming language theory and formal methods.

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

Localized Model Order Reduction for Parameter Optimization with Multiscale PDE Constraints

Explore localized model order reduction techniques for multiscale PDE-constrained optimization, focusing on localized training and on-the-fly enrichment strategies to improve computational efficiency.

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

Achieving Higher-Order Convergence Rates in Numerical Homogenization

Explore advanced multiscale methods for higher-order convergence in numerical homogenization, covering elliptic and time-dependent problems with practical examples.

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

Structure Theorems in Boolean Harmonic Analysis - Part II

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 - Lecture 2

Explore signal recovery techniques using Fourier transforms and restriction theory, with applications to multiple transmissions and continuous problems in mathematics.

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

Inverse Results for Isoperimetric Inequalities - Lecture 4

Explore inverse isoperimetric problems in graphs, focusing on the Fourier-Entropy-Influence conjecture and related inequalities. Progress and applications in PAC learning discussed.

• YouTube
• 1 hour 19 minutes
• On-Demand
• Free Video

Inverse Results for Isoperimetric Inequalities - Lecture 3

Explore inverse isoperimetric problems in graphs, focusing on the Fourier-Entropy-Influence conjecture and related inequalities. Progress and applications discussed.

• YouTube
• 1 hour 11 minutes
• On-Demand
• Free Video

Multiscale Approximations for the Stationary Ginzburg-Landau Equation

Explores discrete minimizers of Ginzburg-Landau energy in finite element spaces, focusing on parameter κ's influence on vortex lattices and mesh resolution conditions for accurate numerical simulations.

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

Dynamic Brittle Fracture as a Well-Posed Nonlocal Initial Value Problem

Explore a nonlocal model for dynamic brittle damage, examining its phases, evolution, and energy balance. Learn how this approach relates to Griffith fracture energy and Navier's equation for crack propagation.

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

Asymptotics of Optimal Constants in the Khinchine-Kahane Inequality

Explore the asymptotics of optimal constants in Khinchine-Kahane inequality, examining classical moment inequalities for Rademacher sums and recent developments in this century-old field of study.

• YouTube
• 1 hour 22 minutes
• On-Demand
• Free Video

Inverse Results for Isoperimetric Inequalities - Part II

Explores inverse isoperimetric problems in graphs, focusing on the Fourier-Entropy-Influence conjecture and related inequalities, with applications to PAC learning and other areas.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video