Overview


Photo by BIRS-IASM

Mats Vermeeren

EPSRC Research Fellow and Lecturer
Department of Mathematical Sciences
Loughborough University

📧 m.vermeeren@lboro.ac.uk

👨‍🏫 University webpage

orcid.org/0000-0002-6982-4505

Google Scholar

Mathstodon.xyz

Youtube Channel

 

Member of the London Mathematical Society
and the International Society of Nonlinear Mathematical  Physics

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.

Maths outreach

An overview of my outreach activities can be found here.

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:

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