Ariadne: A tool for rigorous numerics and verification of nonlinear and hybrid systems. http://www.ariadne-cps.org/
- Fixed-point theories of Lefschetz and Nielsen
- Conley index theory
- Homo/heteroclinic tangles and trellises
- Forcing relations of horseshoe orbits
Control and systems theory
- Foundations of hybrid systems theory
- Observability and realisation of (piecewise-affine) hybrid systems
- Verification of nonlinear hybrid automata
- Semantics of specification languages for hybrid systems
Computability and Complexity
- Computable analysis and topology
- Computable semantics for systems and logics
- Rigorous numerical methods
- Verification of nonlinear and hybrid systems
- Electrophysiology of cardiac myocytes
Professional career history
- January 2011–December 2014: Assistant professor, Department of Knowledge Engineering, Maastricht University
- November 2010–December 2010: Scientific researcher, Dipartimento di Informatica, Universita degli Studi di Verona
- April 2005–March 2010: Scientific researcher, Centrum voor Wiskunde en Informatica, Amsterdam, supported by €600 000 NWO Vernieuwingsimpuls Vidi grant 639.032.408 on “Topological Methods for Systems and Control”.
- January–March 2005: Visiting Research Fellow, Research Institute for Mathematical Sciences, Kyoto
- April 2003–December 2004: Postdoctoral researcher, Centre for Mathematics and Computer Science, Amsterdam on project "Computation and control for hybrid systems"
- January 2000–June 2002: Research Fellow and Lecturer, Department of Mathematical Sciences, University of Liverpool. Supported by Leverhulme Special Research Fellowship SRF/4/9900172 on “Periodic orbits of chaotic systems.”
- August 1995–December 1999: Ph.D. Student in Applied Mathematics, University of California, Berkeley. Thesis “Surface diffeomorphisms with homoclinic and heteroclinic tangles” under the supervision of Prof. Morris Hirsch.