P.J. Collins

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
• Verification of nonlinear and hybrid systems

Systems biology

• Electrophysiology of cardiac myocytes

• 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.