# Events

Events organised by members of the Applied and Computational Mathematics group

A full calendar of events at ICMS is also available.

## Upcoming and Recent Events

### New Directions in Classical Density Functional Theory, 11/05/2020-15/05/2020, ICMS, Edinburgh

Classical density functional theory (DFT) is a microscopic approach for determining the average density distribution of a classical many-particle system in an arbitrary external potential. The approach is embedded in the framework of statistical mechanics and thermodynamics and is extremely powerful: Not only can one use it to accurately determine particle distributions, but one additionally gets thermodynamic quantities such as interfacial tensions, pressures and adsorptions. The applications of DFT have been numerous since its inception in the late 1970's, and in the last couple of decades the area has a renewed vigour thanks to the extension of the theory to cover dynamical non-equilibrium phenomena. This important extension is known as dynamical density functional theory (DDFT).

The goal of this workshop is to bring together the mathematicians, physical scientists, materials scientists, and engineers working on developing and applying DFT and DDFT to discuss recent advances and to stimulate future work.

### Numerical Linear Algebra for PDEs and Large Scale Optimization, 17/02/2020-18/02/2020, Padova

Numerical linear algebra techniques, including the design of efficient preconditioners for iterative methods, form an essential component of solvers for huge-scale problems in the fields of optimization, PDEs and their applications, and many others. In this workshop, partially funded by the CaRiPaRo Visiting Programme** **we focus on the fast and robust solution of linear and nonlinear systems arising from a range of mathematical applications, and new challenges relating to modern optimization problems. The meeting will consist of presentations from a number of leading researchers in numerical linear algebra for Optimization and PDEs, aiming to encourage an exchange of ideas to further advance the state-of-the-art in these fields.

## Past Events

### Advances in Linear Algebra and Huge-Scale Optimization, 01/07/2019-02/07/2019, ICMS, Edinburgh

It is well-established that bespoke numerical linear algebra techniques, including the design of direct and iterative methods, form an essential component of solvers for huge-scale problems in the fields of optimization, PDEs and their applications, and many others. In this workshop we focus on the fast and robust solution of matrix systems arising from a range of mathematical applications, and new challenges relating to modern optimization problems. The meeting will consist of presentations from a number of leading researchers in optimization and numerical linear algebra, aiming to encourage an exchange of ideas to further advance the state-of-the-art in these fields.

### Beyond the discrete: Iterative methods from the continuum perspective, 03/06/2019-07/06/2019, Dublin

A large body of work focuses on analyzing all aspects of the convergence behavior of Krylov subspace methods, developing effective preconditioners for them, and designing new methods. Much of this work has been done from the perspective of the finite dimensional problem, where one implicitly considers the discretization to have no role in the discussion of the iterative methods or how one judges the method to have converged (i.e., in what norm we measure convergence). The majority of the work in the literature takes this approach, but it is by no means universally so. For example, the development of a preconditioner is sometimes guided by properties of the underlying continuous problem or carried out specifically to obtain preconditioned linear systems whose condition number is independent of the discretization mesh. Furthermore, there has been an effort by some authors more recently to approach Krylov subspace methods directly from this continuum perspective. One can then reconsider what the role and interpretation of the preconditioner is and its relationship to the scalar product, with respect to the underlying continuum problem and physics.

### Scottish Numerical Methods Workshop on Stochastic Processes and Applications, 10/05/2019, ICMS, Edinburgh

This is the first workshop of the Scottish Numerical Methods Network 2019. It has a (broad) focus on "Stochastic Processes and Applications", and should be of particular interest to PhD students, postdocs and early-career researchers. The workshop is intended to be accessible to a wide audience, and all are welcome.

### New directions in applied linear algebra, numerical methods for PDEs, and applications, 09/04/2018-11/04/2018, ICMS, Edinburgh

The accurate numerical solution of partial differential equations and optimization problems, including through the use of linear algebra techniques for solving the resulting matrix systems, presents vast challenges for researchers in applied mathematics and engineering. In this workshop, we consider the fast and efficient discretization and solution of PDEs arising from a wide variety of scientific applications, including optimization problems where PDEs act as constraints.

This workshop will consist of presentations from a number of leading researchers, aimed to encourage an exchange of ideas to further advance the state of the art in the numerical solution of PDEs, applied linear algebra, and computational optimization.

### Uncertainty Quantification and Computational Imaging, 23/04/2018-24/04/2018, ICMS, Edinburgh

This workshop will focus on sampling and simulation challenges arising in the field of Uncertainty Quantification (UQ) and its many synergies with the field of computational imaging. In particular, this short workshop will bring together experts from the area of Markov Chain Monte Carlo (MCMC) and from computational imaging in order to exchange ideas that will benefit both areas.

### Data-Driven Modelling of Complex Systems, 08/05/2018-10/05/2018, Alan Turing Institute, London

Complex models in all areas of science and engineering, and in the social sciences, must be reduced to a relatively small number of variables for practical computation and accurate prediction. In general, it is difficult to identify and parameterize the crucial features that must be incorporated into the model, but powerful statistical approaches are becoming available based on analysis of large volumes of data. This is bringing fundamental change in the way we think about models. A new modelling paradigm is emerging based on the combination of statistical inference, high-throughput computation and physical laws, yet the mathematical foundations for combining these methods are still in their infancy.

The purpose of this workshop is to bring together a diverse group of mathematicians and computational scientists to explore new ways of incorporating data analysis into complex systems modelling. Application topics to be discussed include methods for collective dynamics (flocking, schooling and pedestrian models), molecular modelling, cell biology, and fluid dynamics.

The workshop is funded by the Alan Turing Institute.

### Multiscale, Computational Modelling - 2nd Meeting of the Scottish Numerical Methods Network, 16/05/2018, ICMS, Edinburgh

Methods for computing the properties of materials and structures are some of the most widely-used numerical schemes, but are generally much less well studied by mathematicians than by chemists, physicists and engineers. However, many of these methods are extremely amenable to mathematical analysis and such work can, and has, lead to significantly improved algorithms. This meeting will bring together experts in numerical analysis and implementation of simulation algorithms, as well as users in the applied sciences. This will allow mathematicians to be informed of the state-of-the art methods, as well as their limitations, and in turn will allow end users to learn about recent mathematically-driven improvements. We interpret 'materials science' very broadly, from microscopic particle-based (molecular dynamics) methods to meso/macroscopic continuum/statistical mechanics approaches, both in the classical and quantum regimes. We also welcome the participation of experts who believe that their numerical methods may have application in such areas.

### Approximating High-dimensional Functions, 18/12/2017-19/12/2017, Alan Turing Institute, London

Organised by Aretha Teckentrup (a.teckentrup@ed.ac.uk) and Hemant Tyagi (Alan Turing Institute and University of Edinburgh)

Many problems in science and engineering involve an underlying unknown complex process that depends on a large number of parameters. The goal in many applications is to reconstruct, or learn, the unknown process given some direct or indirect observations. Mathematically, such a problem can be reformulated as one of approximating a high dimensional function from limited information available, such as a small number of samples. The workshop will focus on the mathematical foundations of this problem, featuring talks by eminent researchers in the fields of multivariate approximation theory, high-dimensional integration, non-parametric regression and related areas.

The workshop is funded by the Alan Turing Institute.

### MIGSAA Multiscale Problems in Nonlinear PDEs Summer School, 05/09/2017 - 07/09/2017, ICMS, Edinburgh

Organised by Ben Goddard (B.Goddard@ed.ac.uk), Dominic Breit (Heriot-Watt) and Markus Schmuck (Heriot-Watt).

This summer school will provide a broad-ranging introduction to mathematical fluid mechanics, in particular covering the analytical and applied aspects of PDEs arising in the dynamics of viscous flows. Each of the invited speakers will give three 1.5 hour lectures on a topic related to his/her research expertise. The speakers are Lubomir Banas (Bielefeld), Miroslav Bulicek (Charles University Prague) and Christoph Ortner (Warwick).

### Summer School on Mathematical Aspects of Inverse Problems, 29/08/2017-01/09/2017, Alan Turing Institute, London

Organised by Aretha Teckentrup (a.teckentrup@ed.ac.uk) and Claudia Schillings (University of Mannheim).

This summer school will focus on mathematical foundations of inverse problems, at the interface of applied mathematics, statistics and data science.

The school is funded by the Alan Turing Institute.

### MIGSAA Fluid Mechanics Summer School, 13/09/2016 - 15/09/2016, ICMS, Edinburgh

Organised by Ben Goddard (B.Goddard@ed.ac.uk), Dominic Breit (Heriot-Watt) and Markus Schmuck (Heriot-Watt).

This summer school will provide a broad-ranging introduction to mathematical fluid mechanics, in particular covering the analytical and applied aspects of PDEs arising in the dynamics of viscous flows. Each of the invited speakers will give three 1.5 hour lectures on a topic related to his/her research expertise. The speakers are Andeas Munch (Oxford), Eduard Feireisl (Czech Academy of Sciences) and Anne Juel (Manchester).

### Trapped Waves and Wave Radiation in Fluid Mechanics 18/07/2016-22/07/2016, ICMS, Edinburgh

Organised by Lyuba Chumakova (lyuba.chumakova@ed.ac.uk), Paul Milewski (p.a.milewski@bath.ac.uk) (Bath) and Ted Johnson (e.johnson@ucl.ac.uk) (UCL).Trapped waves and wave radiation arise in many research areas ranging from atmosphere-ocean and climate science to water waves and nonlinear optics. They also arise in diverse industrial applications ranging from weather prediction to wave-energy capture and to environmental risk assessment. However, there exists no unified mathematical framework for these wave phenomena. The goal of this workshop is to help create this mathematical framework by merging the approaches used in different application areas. The workshop will bring togetherapplied mathematicians, scientists from national labs and weather-prediction agencies, and industrial partners. To facilitate the exchange of ideas, encourage interdisciplinary and industrial collaborations, the workshop will have fewer academic talks but will incorporate longer discussions following the talks. The workshop will also include an industrial afternoon and a public lecture. If you are interested in participating, please email the organisers.This workshop is sponsored by EPSRC.

### Challenges in Statistical Mechanics: from Mathematics to Molecular Dynamics to Technological Applications 7/12/2015-10/12/2015, Imperial College London

Organised by Ben Goddard (b.goddard@ed.ac.uk), Serafim Kalliadasis (Imperial), Michela Ottobre (Heriot-Watt), Grigorios Pavliotis (Imperial) and Johannes Zimmer (Bath).

The workshop will place a strong emphasis on interdisciplinary approaches to Statistical Mechanics including Molecular Dynamics and in this spirit we aim to bring together researchers from different communities (Chemists, Engineers, Mathematicians and Physicists) to discuss recent advances, ongoing research activities and open problems related to Statistical Mechanics and its numerous applications in natural phenomena and technology.

This workshop is sponsored by EPSRC.

### MCM3: Multiscale Computational Methods in Materials Modelling 16/06/2014-20/06/2014, ICSM, Edinburgh

Organised by Ben Leimkuhler (B.Leimkuhler@ed.ac.uk), R. Harrison (Stony Brook), P. Plechac (Delaware), and S. Plimpton (Sandia National Laboratory).

This event will comprise of a 2-day tutorial, followed by a 3 day meeting. While the scope of the workshop is very broad (spanning quantum, classical and mesoscale techniques) the emphasis will be on mathematical approaches, stochastic numerical algorithms and parallel computing issues. The goal is to seek points in common among scale-bridging techniques in different modelling regimes. The experience of the participants is also expected to be quite broad, with chemists, engineers, physicists and mathematicians all presenting talks on both theoretical and applied topics. Graduate students and postdoctoral researchers are particularly encouraged to attend both the tutorial and the meeting.

This workshop is sponsored by NAIS (the Centre for Numerical Algorithms and Intelligent Software).

### Automated Code Generation 01/07/2014, ICMS, Edinburgh

Organised by James Maddison (j.r.maddison@ed.ac.uk) and Mike Giles (University of Oxford).

This one day workshop on automated code generation will bring together speakers with expertise in the areas of optimised discrete Fourier transforms, parallel computing on Graphics Processing Units (GPU), portable automated code generation techniques on high-performance computing resources, and high-level algorithmic differentiation.

This workshop is sponsored by NAIS (the Centre for Numerical Algorithms and Intelligent Software).

### Maxwell Institute Colloquium on Modelling, Mathematics, and Computationof Complex Multiscale Systems 02/07/2014, 14 India Street, Edinburgh

Organised by Ben Goddard (b.goddard@ed.ac.uk) and Markus Schmuck (Heriot-Watt University).

Complex Multiscale Systems play a crucial and wide-ranging role in daily life; examples include many chemical and biological processes, mechanical and electrical properties of materials, and many modern technologies such as micro- and nano-fluidic systems, batteries, fuel cells, and genetic analysis. Such problems are often of an interdisciplinary nature, and this workshop will reflect the large breadth of interest in multiscale modelling in mathematics and the applied sciences. Despite recent novel and influential mathematical and computational approaches, there are still many open questions regarding such systems. Along with four talks by experts in the field, this meeting will also facilitate the discussion of the current challenges faced by researchers tackling complex multiscale systems.

Invited speakers: Weinan E (Princeton), Gero Friesecke (TU Munich), Ping Lin (Dundee), and Lucia Scardia (Glasgow).

This workshop is sponsored by NAIS (the Centre for Numerical Algorithms and Intelligent Software) and CANPDE (Centre for Analysis and Nonlinear PDEs).

### Maxwell Institute Graduate School on Evolution Equations 08/10/2014-10/10/2014, Edinburgh

Organised by Ben Leimkuhler (B.Leimkuhler@ed.ac.uk), Lehel Banjai and Heiko Gimperlein (Heriot-Watt University).

Jointly organized by Heriot-Watt University and the University of Edinburgh, the school aims to expose postgraduate students and interested faculty to some of the recent developments in the analysis of evolution equations and prepare them for research in these fields. Erwan Faou and Christian Lubich have agreed to give short courses on the analysis of stochastic evolution equations, respectively the long-time behavior of oscillatory Hamiltonian ODEs und PDEs and their numerical discretizations.

The school is supported by the Edinburgh Mathematical Society and the Glasgow Mathematical Journal Trust Fund.

### Maxwell Colloquium on Topological Fluid Dynamics 12/03/2014, ICMS, Edinburgh

Organised by Michal Branicki (M.Branicki@ed.ac.uk) and Simon Malham (Heriot-Watt University).

Understanding the topological structure of fluid flows is key for tackling many fundamental issues in fluid dynamics, including the possible finite time ‘blow-up’ in the incompressible three-dimensional Euler and Navier–Stokes equations. Recent theoretical, numerical and experimental research has highlighted the plethora of such coherent structures in real flows beyond vortex tubes and sheets, including vortex rings, trefoil vortex knots and fluid-fluid surface cusps.

This one day meeting brings together five experts in the area and aims to develop links to other areas of mathematics and computational sciences in the hope to provide new insight and new approaches to the analysis of complex turbulent flows.

Invited speakers: Bob Kerr (Warwick), John Gibbon (Imperial), Keith Moffat (Cambridge) and Robert Krasny (Michigan).