Hausdorff Center for Mathematics Courses

Parametric PDEs - Numerical Methods for Forward UQ and Surrogate Modelling - Part I

Explore numerical methods for uncertainty quantification in parametric PDEs, covering surrogate modeling, stochastic collocation, and adaptive multilevel approaches for efficient forward UQ.

• YouTube
• 1 hour 35 minutes
• Self-Paced
• Free Video

An Introduction to Multiscale Methods and Localised Model Reduction - Part IV

Explore advanced multiscale methods and localised model reduction for solving PDEs with coefficients varying across multiple scales using GFEM frameworks.

• YouTube
• 1 hour 39 minutes
• Self-Paced
• Free Video

Parametric PDEs - Numerical Methods for Forward UQ and Surrogate Modelling - Part III

Explore advanced adaptive multilevel approaches and a posteriori error estimation for parametric PDEs with uncertain inputs in forward uncertainty quantification.

• YouTube
• 1 hour 34 minutes
• Self-Paced
• Free Video

Multilevel Monte Carlo Methods for Random Differential Equations - Part III

Explore advanced Multilevel Monte Carlo techniques for solving random differential equations with uncertainty, covering optimization and data assimilation applications.

• YouTube
• 1 hour 4 minutes
• Self-Paced
• Free Video

Multilevel Monte Carlo Methods for Random Differential Equations - Part IV

Master Multilevel Monte Carlo techniques for random differential equations, focusing on PDE optimization under uncertainty and sequential data assimilation applications.

• YouTube
• 1 hour 23 minutes
• Self-Paced
• Free Video

Multilevel Monte Carlo Methods for Random Differential Equations - Part I

Discover multilevel Monte Carlo methods for solving random differential equations with uncertainty in model parameters and stochastic fluctuations.

• YouTube
• 1 hour 10 minutes
• Self-Paced
• Free Video

Multilevel Monte Carlo Methods for Random Differential Equations - Part II

Explore advanced Multilevel Monte Carlo techniques for solving random differential equations, covering PDE optimization under uncertainty and sequential data assimilation applications.

• YouTube
• 1 hour 28 minutes
• Self-Paced
• Free Video

An Introduction to Multiscale Methods and Localised Model Reduction - Part III

Explore advanced multiscale methods for solving PDEs with coefficients varying across multiple scales using Generalised Finite Element Methods and localised model reduction.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

An Introduction to Multiscale Methods and Localised Model Reduction - Part I

Explore advanced computational techniques for solving PDEs with multiscale coefficients using Generalised Finite Element Methods and localised model reduction frameworks.

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

The Quadratic Littlewood-Offord Problem

Explore the quadratic Littlewood-Offord problem and discover optimal bounds for concentration of quadratic polynomials with random variables in this advanced mathematics lecture.

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

Multilevel Markov Chain and Interacting Particle Methods for Bayesian Inverse Problems

Discover advanced multilevel Markov chain and particle methods for solving complex Bayesian inverse problems in computational mathematics.

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

Multilevel Sequential Monte Carlo for Bayesian Inverse Problems with Random Likelihoods

Explore multilevel sequential Monte Carlo methods for efficiently solving Bayesian inverse problems with Monte Carlo-approximated likelihoods in uncertainty quantification.

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

Multilevel Monte Carlo Methods with Smoothing

Discover advanced multilevel Monte Carlo techniques with smoothing for solving PDEs with uncertain parameters, featuring circulant embedding methods to optimize computational efficiency.

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

Sparse Multi-Level Approximations for PDE-Constrained Optimization Under Uncertainty

Discover advanced multilevel quadrature methods for solving PDE-constrained optimization problems with uncertainty while preserving convexity and reducing computational costs.

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

Elliptic Curves and Definability Over Big Rings

Explore rank stability results and their implications for definability over big subrings of number fields through elliptic curve theory.

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