**Mats Vermeeren**

**EPSRC Research Fellow and LecturerDepartment of Mathematical Sciences Loughborough University**

## Academic background

I started my studies in mathematics at the KU Leuven in Belgium, my native country. After obtaining a bachelor’s degree there in 2012 I moved to Berlin to enter the graduate program of Berlin Mathematical school. I joined the geometry and mathematical physics research group at the Technische Universität Berlin and obtained a master’s degree (2014) and a doctorate (2018). In 2020 and 2021 I was a DFG Research Fellow at the University of Leeds, UK. In 2022 I started a Doctoral Prize Fellowship at Loughborough University. Currently, I am a Lecturer at Loughborough University and hold an EPSRC Open Plus Fellowship.

## Research Interests

My research is centered around the Lagrangian structure (in the sense of variational principles) of discrete and continuous dynamical systems and their symmetries.

### Integrable systems

Much of my work deals with integrable systems, which are differential equations (or difference equations) that exhibit a surprising amount of structure. While integrable differntial equations are usually described in a Hamiltonian framework, they allow a beautiful variational principle too:

- Variational principles for integrable systems:
*Lagrangian multiform*theory /*pluri-Lagrangian*systems.

Lagrangian multiform theory applies to discrete as well as continuous integrable systems. More broadly I am intersted in connections between these two realms:

- Hierarchies of integrable differential equations as continuum limits of fully discrete equations.

[*You can find a layman’s introduction to integrable systems in this blog post; and an introduction assuming some mathematical background in these slides.*]

### Geometric numerical integration

Most differential equations cannot be solved exactly. In practice they are approximated numerically. When a differential equation has some structure (in an abstract geometric sense), an effective way to improve the efficiency of the numerical methods is to ensure they preserve this structure. Such a numerical algorithm is known as a gemetric numerical integrator. My main interests in this area are:

- Backward error analysis for variational integrators.
- Discretization of contact Hamiltonian systems.

[*You can find a light-hearted introduction to geometric numerical integration, assuming some mathematical background, in these slides: A picture book of geometric numerical integration.*]

### More details

See the list of my publications and the list of talks I’ve given

## Fellowships and Research Projects

- EPSRC Open Plus Fellowship: Lagrangian Multiforms for Symmetries and Integrability: Classification, Geometry, and Applications
- DFG Research Fellowship: Lagrangian Theory of Integrable Hierarchies: Connections and Applications (2020-2021)

- SFB Transregio 109: Discretization in Geometry and Dynamics, in particular the projects

B2, Discrete Multidimensional Integrable Systems: Geometry and Algebra (2016-2019)

and

B4, Discretization as Perturbation: Qualitative and Quantitative Aspects (2015-2016)