Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

 

Past events in this series


Thu, 22 May 2025

14:00 - 15:00
Lecture Room 3

When you truncate an infinite equation, what happens to the leftovers?

Geoff Vasil
(University of Edinburgh)
Abstract

Numerically solving PDEs typically requires compressing infinite information into a finite system of algebraic equations. Pragmatically, we usually follow a recipe: “Assume solutions of form X; substitute into PDE Y; discard terms by rule Z.” In contrast, Lanczos’s pioneering “tau method” prescribes modifying the PDE to form an exact finite system. Crucially, any recipe-based method can be viewed as adding a small equation correction, enabling us to compare multiple schemes independently of the solver. 

This talk also addresses a paradox: PDEs often admit infinitely many solutions, but finite systems produce only a finite set. When we include a “small” correction, the missing solutions are effectively hidden. I will discuss how tau methods frame this perspective and outline proposals for systematically studying and optimising various residuals.

Thu, 29 May 2025

14:00 - 15:00
Lecture Room 3

On the data-sparsity of the solution of Riccati equations with quasiseparable coefficients

Stefano Massei
(Universita di Pisa)
Abstract

Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in various control theory applications. 

This work demonstrates that when the matrix coefficients of the equation are quasiseparable, the solution also exhibits numerical quasiseparability. This property enables us to develop two efficient Riccati solvers. The first solver is applicable to the general quasiseparable case, while the second is tailored to the particular case of banded coefficients. Numerical experiments confirm the effectiveness of the proposed algorithms on both synthetic examples and case studies from the control of partial differential equations and agent-based models. 

Thu, 05 Jun 2025
14:00
Lecture Room 3

Solving sparse linear systems using quantum computing algorithms

Leigh Lapworth
(Rolls-Royce)
Abstract

The currently available quantum computers fall into the NISQ (Noisy Intermediate Scale Quantum) regime. These enable variational algorithms with a relatively small number of free parameters. We are now entering the FTQC (Fault Tolerant Quantum Computer)  regime where gate fidelities are high enough that error-correction schemes are effective. The UK Quantum Missions include the target for a FTQC device that can perform a million operations by 2028, and a trillion operations by 2035.

 

This talk will present the outcomes from assessments of  two quantum linear equation solvers for FTQCs– the Harrow–Hassidim–Lloyd (HHL) and the Quantum Singular Value Transform (QSVT) algorithms. These have used sample matrices from a Computational Fluid Dynamics (CFD) testcase. The quantum solvers have also been embedded with an outer non-linear solver to judge their impact on convergence. The analysis uses circuit emulation and is used to judge the FTQC requirements to deliver quantum utility.

Thu, 12 Jun 2025

14:00 - 15:00
Lecture Room 3

Finite volumes for a generalized Poisson-Nernst-Planck system with cross-diffusion and size exclusion

Clément Cancès
(INRIA LILLE)
Abstract

We propose and analyse two structure preserving finite volume schemes to approximate the solutions to a cross-diffusion system with self-consistent electric interactions introduced by Burger, Schlake & Wolfram (2012). This system has been derived thanks to probabilistic arguments and admits a thermodynamically motivated Lyapunov functional that is preserved by suitable two-point flux finite volume approximations. This allows to carry out the mathematical analysis of two schemes to be compared.

This is joint work with Maxime Herda and Annamaria Massimini.

 

 

Thu, 19 Jun 2025
14:00
Lecture Room 3

Hilbert’s 19th problem and discrete De Giorgi-Nash-Moser theory: analysis and applications

Endre Süli
(Mathematical Institute (University of Oxford))
Abstract
This talk is concerned with the construction and mathematical analysis of a system of nonlinear partial differential equations featuring in a model of an incompressible non-Newtonian fluid, the synovial fluid, contained in the cavities of human joints. To prove the convergence of the numerical method one has to develop a discrete counterpart of the De Giorgi-Nash-Moser theorem, which guarantees a uniform bound on the sequence of continuous piecewise linear finite element approximations in a Hölder norm, for divergence-form uniformly elliptic partial differential equations with measurable coefficients.