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P.J. Collins

Since 2011 I have been an Assistant Professor at the Department of Advanced Computing Sciences (DACS) at Maastricht University. I am a member of the Systems & Control and the Algorithms research teams, and was co-leader of the Explainable and Reliable Artificial Intelligence (ERAI) from 2018 to 2021. I obtained my Ph.D. in Applied Mathematics from the University of California at Berkeley in 1999.

My main research interest is formal methods for the analysis and verification of nonlinear and hybrid dynamic systems. I am one of the main developers of Ariadne, a C++/Python library for formal verification of cyber-physical systems, which is a joint project with the University of Verona. 

  • Mathematical analysis of chaotic dynamical systems and hybrid control systems using topological methods to compute symbolic abstractions.
  • Theoretical computability foundations for continuous mathematics, and the use of proof assistants to verify theory and algorithms.
  • Methods for rigorous numerical calculation and their implementation,
  • Applications, notably in systems biology.

 

Expertises

Software

Ariadne: A tool for rigorous numerics and verification of nonlinear and hybrid systems. http://www.ariadne-cps.org/

Topological dynamics

  • 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
  • Formal proofs in systems theory and rigorous numerics.

Systems biology

  • Electrophysiology of cardiac myocytes

 

Career history
  • January 2011– : 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.