Overview

DFG Research Fellow at the School of Mathematics of the University of Leeds

📧 m.vermeeren@leeds.ac.uk

orcid.org/0000-0002-6982-4505

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). (The respective theses can be found on the publications page.) Since January 2020 I am a postdoc in the integrable systems group at the University of Leeds, UK.

Research Interests

My research is centered around Lagrangian (i.e. variational) dynamical systems and can be broadly divided in two areas. One area involves geometric numerical integration of Lagrangian systems, that is variational integrators. The second part deals with integrable systems. While integrable ODEs or hierarchies of PDEs are usually described in a Hamiltonian framework, but allow a beautiful variational principle too.

Integrable systems

  • Variational principles for continuous and discrete integrable systems: pluri-Lagrangian or Lagrangian multiform theory
  • Hierarchies of integrable differential equations as continuum limits of fully discrete equations

(You can find an introduction to integrable systems, assuming some mathematical background, in these slides: What is… an integrable system?)

Geometric numerical integration

  • 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

Projects

Current

DFG Research Fellowship: Lagrangian Theory of Integrable Hierarchies: Connections and Applications

Past

SFB Transregio 109: Discretization in Geometry and Dynamics

In particular the projects
B2, Discrete Multidimensional Integrable Systems: Geometry and Algebra (2015-2016)
and
B4, Discretization as Perturbation: Qualitative and Quantitative Aspects (2016-2019)