The University of Bath SIAM-IMA Student Chapter hosted the SIAM UKIE National Student Chapter Conference in 2018, bringing together students working in all areas of applied and industrial mathematics, and related fields, from across the UK and Ireland.

There were opportunities for students to showcase their research through a talk or a poster, and to hear talks by distinguished plenary speakers. The conference included 4 plenary talks, 29 contributed talks and 23 contributed posters, and was attended by 104 registered participants from 25 different institutions.

The organisers would like to thank all participants for making this conference a success.

The programme will comprise sessions of student talks and posters, and four plenary talks from the folowing speakers:

- Marta Blangiardo (Imperial College London) —
*Modelling spatio-temporal data: methods, examples and challenges*; - Simon Chandler-Wilde (University of Reading) —
*Coercivity of second kind boundary integral equations on Lipschitz domains*; - Ian Griffiths (University of Oxford) —
*iPhones and Dysons: using fluid dynamics to tailor technology*; - Nicole Spillane (École Polytechnique) —
*Domain Decomposition Methods with Adaptive Multipreconditioning*.

This is a summary of the programme. Download the full conference programme for more details, including talk and poster abstracts.

Monday 18th June | Tuesday 19th June | ||||
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08:30 — 09:00 | COFFEE4 West Atrium |
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09:00 — 10:15 | SESSION 3AOliver Dunbar Daoping Zhang 4 West 1.2 |
SESSION 3BAoife Hill Hannah Conroy Broderick Paul Greaney Wolfson Lecture Theatre |
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10:00 — 10:30 | COFFEE & REGISTRATION4 West Atrium |
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10:30 — 11:45 | WelcomePlenary Talk - Nicole SpillaneDomain Decomposition Methods with Adaptive MultipreconditioningUniversity Hall |
10:15 — 10:45 | COFFEE4 West Atrium |
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10:45 — 11:45 | Plenary Talk - Ian GriffithsiPhones and Dysons: using fluid dynamics to tailor technologyUniversity Hall |
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11:45 — 13:00 | SESSION 1ASean Hon Hassan Izanloo Nikoleta Glynatsi 4 West 1.2 |
SESSION 1BEoghan Staunton Tsz Yan Leung Wakil Sarfaraz Wolfson Lecture Theatre |
11:45 — 13:00 | SESSION 4ARóisín Hill Bartosz Jaroszkowski Leonardo Rocchi 4 West 1.2 |
SESSION 4BEnrico Gavagnin Lisa Maria Kreusser Jehan Alswaihli Wolfson Lecture Theatre |

13:00 — 14:00 | LUNCH4 West Atrium |
13:00 — 14:00 | LUNCH4 West Atrium |
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14:00 — 15:15 | SESSION 2AHang Liu Luke Smallman Adam Barker 4 West 1.2 |
SESSION 2BDanny Groves Martina Cracco Dane Grundy Wolfson Lecture Theatre |
14:00 — 15:15 | SESSION 5AYiannis Simillides Sarah Roggendorf Anitgoni Kleanthous 4 West 1.2 |
SESSION 5BQays Shakir Helena Stage Roberto Galizia Wolfson Lecture Theatre |

15:15 — 15:45 | COFFEE4 West Atrium |
15:15 — 16:30 | Plenary Talk - Simon Chandler-WildeCoercivity of second kind boundary integral equations on Lipschitz domainsUniversity HallClose |
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15:45 — 16:45 | Plenary Talk - Marta BlangiardoModelling spatio-temporal data: methods, examples and challengesUniversity Hall |
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16:45 — 18:30 | Poster Session& Wine Reception 4 West Atrium |
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19:30 | DINNERWessex Restaurant |

In addition to the conference dinner on the Monday evening, we organised social events on both the Sunday and Tuesday, for any participants who wish to stay in Bath for an extra evening:

**Sunday evening:**Drinks in the Bell Inn, Walcot Street, from 20:00, to welcome participants arriving on Sunday.**Tuesday afternoon:**Walking tour of the city of Bath, setting off from the university campus at approximately 17:00.

**Modelling spatio-temporal data: methods, examples and challenges** (PDF)

*Monday 18th June, 15:45 – University Hall*

In this talk I will present how the Bayesian hierarchical framework is commonly used to model spatial and spatio-temporal data. I will first consider the space as discrete (small area framework) and introduce autoregressive structures, which can be used to account for spatial and temporal dependency. I will focus on different examples drawn from the epidemiological field.

Then I will move to the case when space is continuous and introduce the geostatistics framework. Here I will present two examples drawn from epidemiology and environmental science.

I will finish the talk presenting some of the (methodological and non) challenges which researchers face in this context.

**Coercivity of second kind boundary integral equations on Lipschitz domains** (PDF)

*Tuesday 19th June, 15:15 – University Hall*

Boundary integral equation methods are a well-established technique for solving linear elliptic partial differential equations. Second kind integral equation formulations, taking the form \(\phi + K\phi = g\), where \(K\) is a boundary integral operator, are attractive because they are well-conditioned. However, it is not known whether standard Galerkin numerical methods are stable and convergent for these formulations for Laplace's equation with Dirichlet boundary conditions on general Lipschitz domains. When the domain \(D\) is bounded, smooth, and convex the standard second kind integral equation formulation for this simplest case can be written in this form where \(K\) is a contraction, i.e. \(\|K\|<1\). Under certain other conditions on \(D\) it is known that \(K=L+C\), with \(\|L\|<1\) and \(C\) compact, but it is a long-standing conjecture that this holds for all Lipschitz \(D\). Both these conditions guarantee convergence of Galerkin approximation methods.

But in this talk we exhibit examples of Lipschitz domains in 2D for which it does not hold that \(K\) is a compact perturbation of a contraction; in fact the so-called essential norm may be arbitrarily large. On the other hand, in a positive direction, we also exhibit new, modified versions of the standard second kind integral equation formulation which have the attractive property that the associated operators are coercive for all Lipschitz \(D\), so that every Galerkin method is convergent.

Boundary integral equation methods are a well-established technique for solving linear elliptic partial differential equations. Second kind integral equation formulations, taking the form \(\phi + K\phi = g\), where \(K\) is a boundary integral operator, are attractive because they are well-conditioned. However, even in the simplest case (Laplace's equation on a bounded domain \(D\) with Dirichlet boundary conditions), it is not known whether standard Galerkin numerical methods, for example so-called boundary element methods based on finite-element-type approximations, are stable and convergent for these formulations for general Lipschitz domains.

**iPhones and Dysons: using fluid dynamics to tailor technology** (PDF)

*Tuesday 19th June, 10:45 – University Hall*

As technology continues to advance, new strategies involving a range of scientific disciplines are required. Mathematicians can provide frameworks to predict operating regimes and manufacture techniques. In this talk we present two case studies: the fabrication of precision glass, for smartphones and new flexible devices; and the development of superior filters for vacuum cleaners. In each case we use asymptotic analysis to derive a model that determines the fabrication protocol required to produce a desired final product.

**Domain Decomposition Methods with Adaptive Multipreconditioning** (PDF)

*Monday 18th June, 10:30 – University Hall*

Domain decomposition methods are a family of parallel solvers for large linear systems. They all share the idea of approximating the inverse of some matrix by a sum of local inverses (in the so-called subdomains). I will present some classical domain decomposition methods, their limitations and some recent efforts to improve their robustness and scalability so that they can be applied to problems arising from real life simulations.

More precisely, I will present the method of adaptive multipreconditioning. This is a modification of the iterative solver (the preconditioned conjugate gradient algorithm). Instead of one single preconditioner, a family of preconditioners is applied at each iteration, each corresponding to one of the subdomains. This significantly increases the size of the minimization space and consequently accelerates convergence. I will introduce the method, discuss its analysis and show numerical results obtained in collaboration with C. Bovet, P. Gosselet and A. Parret-Fréaud.

Abstracts are available in the conference programme.

**Circulant preconditioners for functions of Toeplitz matrices**

**\((P,w)\)-Partition and alternating sign matrices** (PDF)

**Training memory one strategies for the Prisoner's Dilemma** (PDF)

**Noise and Bistability in the Square Root Map** (PDF)

**Finite or infinite predictability horizon?** (PDF)

**The geometric influence of domain-size on the dynamics of reaction-diffusion systems with applications in pattern formation** (PDF)

**On the computation and application of M-estimators and its bootstrapped version in GARCH models**

**Sparse Principal Component Analysis for Exponential Family Data** (PDF)

**Transience and Recurrence of Markov Processes with Constrained Local Time** (PDF)

**Droplet Spreading, Chemically Treated Surfaces and Mathematics** (PDF)

**Linear stability and transient behaviour of viscoelastic fluids in boundary layers** (PDF)

**The Effect of Surface Stress on Interfacial Solitary Waves** (PDF)

**What Lies Beneath?** (PDF)

**Variational Diffeomorphic Models for Image Registration** (PDF)

**Modelling the evolving ductility of biodegradable polymers** (PDF)

**Wrinkling in soft dielectric plates** (PDF)

**Inhomogeneous Thinning and Breakdown of Thin Dielectric Elastomers** (PDF)

**Adaptive a posteriori meshes for differential equations** (PDF)

**Numerical solution of Isaacs equation** (PDF)

**An efficient adaptive algorithm for elliptic problems with random input data** (PDF)

**The invasion speed of cell migration models with a multi-stage cell-cycle representation** (PDF)

**An Anisotropic Interaction Model for Simulating Fingerprints** (PDF)

**Kernel Reconstruction for Delayed Neural Field Equations**

**FEniCS.jl, solving PDE's using Julia** (PDF)

**Eliminating Gibbs Phenomenon: A non-linear Petrov-Galerkin method for convection-dominated problems** (PDF)

**Light scattering by complex ice crystals using the Boundary Element Method** (PDF)

**\((2,2)\)-Tight Surface Graphs** (PDF)

**Anomalous metapopulation dynamics on scale-free networks** (PDF)

**Phase transitions of multistable dynamical networks**

Abstracts are available in the conference programme.

**Kernel Reconstruction for Delayed Neural Field Equations**

**Discretisation of Wasserstein Gradient Flows for Solving Higher Order Nonlinear Partial Differential Equations**

**Finding and verifying the nucleolus of cooperative games**

**Machine Learning for Image Analysis**

**Navier-Stokes-Korteweg Simulations of Dynamic Wetting using the PeTS Equation of State**

**An Introduction to Horizontal Mean Curvature Flow**

**Droplet Spreading, Chemically Treated Surfaces and Mathematics**

**Decay of Solitary Waves**

**Active Subspaces in Networks**

**Biased Consensus Games**

**Topology optimization of frame structures**

** Nonisothermal & Compressible Viscoelastic fluid Modelling**

**Stability of Oscillatory Rotating Disk Boundary Layers**

**A Contour Integral Eigensolver for Dense Nonlinear Eigenvalue Problems**

**Optimising 'First In Human' trials through dynamic programming**

**Tightness of Surface Graphs**

**The auxiliary region method: simulating second-order systems**

**Cancer Research using Drop-seq data**

**Solving PDEs using Residual Minimization in Discrete Dual Non-Hilbert Norms**

**Mathematically Modelling Indoor WiFi Propagation**

Waleed Ali (University of Bath) | Jehan Alswaihli (University of Reading) | Nifeen Altaweel (Lancaster University) |

Max Antson (University of Bath) | Blake Ashworth (University of Sussex) | Adam Barker (University of Reading) |

Marton Benedek (University of Southampton) | Jack Betteridge (University of Bath) | Hanson Bharth (University of Warwick) |

Sayan Biswas (University of Bath) | Marta Blangiardo (Imperial College London) | Beth Boulton (University of Bath) |

Aoibheann Brady (University of Bath) | Vlad Brebeanu (University of Bath) | Chris Budd (University of Bath) |

Mehmet Siddik Cadirci (Cardiff University) | Alice Callegaro (University of Bath) | James Campbell (Cardiff University ) |

Joel Cawte (University of Bath) | Simon Chandler-Wilde (University of Reading) | Kei Tsi Daniel Cheng (Institute of Mathematics and its Applications) |

Hannah Conroy Broderick (National University of Ireland, Galway) | Martina Cracco (Cardiff University) | Francisco de Melo Viríssimo (University of Bath) |

Zoe Dennison (University of Bath) | Felix Diewald (University of Nottingham) | Joey Dixon (MyLife Digital) |

Zhao Dong (University of Bath) | Oliver Dunbar (University of Warwick) | Rebecca Ellis (University of Bath) |

Thomas Finn (University of Bath) | Melina Freitag (University of Bath) | Roberto Galizia (National University of Ireland, Galway) |

Enrico Gavagnin (University of Bath) | Adam George (University of Bath) | Nikoleta E. Glynatsi (Cardiff University) |

Raffaele Grande (Cardiff University) | Paul Greaney (National University of Ireland, Galway) | Dan Green (University of Bath) |

Matthew Griffith (University of Bath) | Ian Griffiths (University of Oxford) | Danny Groves (Cardiff University) |

Dane Grundy (University of East Anglia) | Leonard Hardiman (University of Bath) | Elli Heyes (University of Bath) |

Aoife Hill (National University of Ireland, Galway) | Róisín Hill (National University of Ireland, Galway) | Sean Hon (University of Oxford) |

Emma Horton (University of Bath) | Emily Hunt (University of Bath) | Hassan Izanloo (Cardiff University) |

Bartosz Jaroszkowski (University of Sussex) | Natasha Javed (University of Bath) | |

Nadeen Khaleel (University of Bath) | Matthias Klar (University of Bath) | Antigoni Kleanthous (UCL) |

David Kohan Marzagão (King's College London) | Antiopi Koronaki (University of Bath) | Lisa Maria Kreusser (University of Cambridge) |

Tadas Krikstanavicius (University of Strathclyde) | Daniel Lagos (University of Bristol) | Andrea Lelli (University of Bath) |

Tsz Yan Leung (University of Reading) | Hang Liu (Lancaster University) | Bas Lodewijks (University of Bath) |

Alex Mackay (Cardiff University ) | Arron Mallinson-Pocock (University of Bath) | Christine Marshall (National University of Ireland, Galway) |

Amy Middleton (University of Bath) | Sam Moore (University of Bath) | Scott Morgan (Cardiff University) |

Kgomotso Morupisi (University of Bath) | Gian Maria Negri Porzio (The University of Manchester) | Daniel Ng (University of Bath) |

Matt Parkinson (University of Bath) | Robbie Peck (University of Bath) | Owen Pembery (University of Bath) |

Aaron Pim (University of Bath) | Lizzi Pitt (University of Bath) | Martin Prigent (University of Bath) |

Benjamin Robinson (University of Bath) | Leonardo Rocchi (University of Birmingham) | Sarah Roggendorf (University of Nottingham) |

Wakil Sarfaraz (University of Sussex) | Qays Shakir (National University of Ireland, Galway) | Yiannis Simillides (UCL) |

Luke Smallman (Cardiff University) | Tom Smith (University of Bath) | Cameron Smith (University of Bath) |

Nicole Spillane (École Polytechnique) | Helena Stage (The University of Manchester) | Eoghan Staunton (National University of Ireland, Galway) |

Annika Stechemesser (University of Warwick) | Ruaridh Thomson (MyLife Digital) | Erica Tyson (Institute of Mathematics and its Applications) |

Sunny Vaghela (King's College London) | Kris van der Zee (University of Nottingham) | Abigail Verschueren (University of Bath) |

Byron Williams (Cardiff University) | Hayley Wragg (University of Bath) | Fedra Zaribaf (University of Bath) |

Daoping Zhang (University of Liverpool) | Lizhi Zhang (University of Bath) |

*We follow both the SIAM Statement on Inclusiveness and the IMA Diversity Statements, and we endeavour to create a welcoming and inclusive atmosphere at the conference, with a diverse range of participants. Students from groups which are underrepresented in the mathematical sciences are particularly encouraged to attend.*

This conference is kindly supported by grants from:

**Society for Industrial and Applied Mathematics (SIAM);****Institute of Mathematics and its Applications (IMA);****Doctoral College, University of Bath**;**Institute for Mathematical Innovation (IMI), University of Bath**;**Department of Mathematical Sciences, University of Bath**.

We are also grateful for support from our industrial sponsors:

The conference was held in the Department of Mathematical Sciences (marked as 4W on this campus map).

The address is:

Department of Mathematical Sciences

4 West

University of Bath

Claverton Down

Bath

BA2 7AY

See the university's guide on how to find us.

Also see this map of the key conference locations and transport links.

If you are arriving by train, you should arrive at Bath Spa train stations. You can then take the U1 bus to the university from Dorchester Street (opposite the station to the left), or walk to the university in 30-40 minutes (up quite a steep hill!).

Coming from Bristol airport, take the A4 bus to Bath, which brings you to the train station, from where you can walk or take a bus, as described above.

If you plan to drive to the university, limited visitor parking spaces are available on campus. See the university's guide to parking on campus.