# Research team

### Oliver Wright (PhD student, 2019–)

Research topic: Partial Differential Equations Modelling Collective Behaviour.

Real-world systems in socio-economics and life sciences often consist of a large number of interacting individuals. These interactions frequently result in formation of complex patterns and collective behaviour, such as aggregation or segregation. Mathematical methods from kinetic theory and mean-field models allow to describe and analyse the distribution of the individuals and derive macroscopic quantities from them. Then, suitable limit partial differential equations which govern these quantities can be derived, analysed and solved numerically.

# Former team members

### Michele Mascherpa (visiting Erasmus student, 2020)

Research topic: Kinetic models for wealth distribution and taxation

Michele, an MSc student at the University of Pavia, Italy, was visiting for four months in spring 2020.

### Dr Blake Ashworth (PhD student, 2016–2019)

In his thesis, Blake develops and investigates numerical methods for partial differential equations with a gradient flow structure with respect to the Wasserstein metric.

### Dr Alexander Pitkin (PhD student, 2015–2019)

In his thesis, Alex derives and analyses high-order methods for partial-integro differential equations arising in computational finance, e.g. Bates model, using efficient high-order compact finite differences.

Alex is working as a proprietary trader.

### Dr James Miles (PhD student, 2014–2018)

Option pricing problems in financial mathematics often lead to parabolic partial (integro-) differential equations. In his thesis, James considers high order dimensional splitting methods for parabolic partial differential equations with mixed second order derivative terms. Further, he considers optimal control problems for option pricing partial-integro differential equations to solve the inverse problem of calibrating option pricing models to observed market prices.

James is working as a data engineer.

### Dr David McCormick (Research fellow, 2015–2018)

Research expertise: Nonlinear partial differential equations

David is interested in developing novel numerical methods which exploit the gradient flow structure in certain nonlinear higher-order partial differential equations as well as in the analysis of the Navier-Stokes equations and the equations of magnetohydrodynamics (MHD).

David is working as an operational planning consultant.

### Dr Michael Taylor (Teaching fellow, 2015–2018)

Mick taught different undergraduate modules, funded by my Leverhulme Trust
Research Project Grant *Novel discretisations for higher-order nonlinear PDE.*

Mick's research interests are in mathematical biology, more specifically in epidemic models on graphs and networks.

He is a teaching fellow at Department of Mathematics, University of Sussex.

### Dr Marco Torregrossa (visiting PhD student from University of Pavia, 2017)

Research topic: Kinetic models of socio-economic phenomena

Marco's research is concerned with the modelling and analysis of socio-economic systems of many interacting agents, using methods from kinetic theory, mathematical physics and analysis.

Marco was a PhD student in the group of Prof Giuseppe Toscani at the University of Pavia, Italy, and visited Sussex for three months in autumn 2017.

### Dr Lara Trussardi (visiting PhD student from Vienna University of Technology, 2014, 2015)

Research topic: Kinetic modelling of herding in financial markets

Lara was a Marie Curie Actions early stage researcher (PhD student) in Prof Jüngel's group at Technische Universität Wien, Austria, financed by the Multi-ITN Novel Methods in Computational Finance (STRIKE).

Lara stayed at Sussex for two months in 2014 and 2015. She is now a postdoctoral research fellow at University of Vienna.

### Dr Christof Heuer (PhD student, 2011–2014)

Christof's thesis covers the derivation, numerical analysis and implementation of high-order compact finite difference schemes for parabolic partial differential equations with mixed derivative terms in multiple spatial dimensions. The resulting schemes are applied to equations arising in computational finance.

Christof is working in the financial consultancy industry.

### Dr Philipp Fuchs (visiting PhD student from Vienna University of Technology, 2012)

Thesis: Underlying metric structures of some evolution equations with focus on the Wasserstein distance

Philipp's thesis investigates various evolution equations from different “metric” points of view. In particular, he studies numerical methods for partial differential equations with a gradient flow structure with respect to the Wasserstein metric.

Philipp was a member of Prof Jüngel's group at Technische Universität Wien, Austria and graduated in 2015.