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Alex Athorne
Sajjad Bakrani Balani
Giulia Carigi
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Maximilian Engel
Federico Graceffa
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MAXIMILIAN ENGEL

Maximilian Engel

PhD Student

 
 

Room: 6M09 Huxley Building

About Me

I am a PhD student at the mathematics department of Imperial College London doing my research in the DynamIC group and being supervised by Jeroen Lamb and Martin Rasmussen. I did a B.Sc. in Economics and a B.Sc. in Maths (with a thesis about essential self-adjointness of (Schrödinger) operators ) at Ludwig-Maximilians-University Munich. Further, I took an M.Sc. degree in Applied Maths at Imperial College. My master thesis addressed the numerical analysis of a coagulation-fragmentation model in animal group size statistics. Furthermore I graduated with an M.A. in philosophy from Hochschule f. Philosophie Munich with a thesis about Whitehead's metaphysics as an ontological framework for quantum mechanics.

Research Interests

My PhD research is focused on stochastic bifurcation theory. In particular, I am approaching the problem of the effects of random perturbations on systems exhibiting a Hopf bifurcation, working within the framework of random dynamical systems. Some of the topics involved are:
  • Stochastic and random differential equations
  • Smooth ergodic theory
  • Random attractors
  • Transitions between order and chaos
  • Diffusion with absorption at the boundary

Papers

  • Thai Son Doan, Maximilian Engel, Jeroen S.W. Lamb, and Martin Rasmussen, Hopf bifurcation with additive noise. DynamIC Preprint 2017-2
  • Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Bifurcation analysis of a stochastically driven limit cycle. DynamIC Preprint 2016-6
  • Pierre Degond and Maximilian Engel, Numerical approximation of a coagulation-fragmentation model for animal group size statistics, Networks and Heterogeneous Media 12, 2 (2017), 217−243. Article MathSciNet Preprint

Working papers

  • M. Engel, A random dynamical systems perspective on killed Markov processes, in preparation.
  • P. Degond, M. Engel, J.-G. Liu and R.L. Pego, A jump process approach to animal group size statistics, in preparation.

Research Talks

  • 14/09/2017: Courant Insitute, NYU, Dynamics Seminar: Quasi-stationary dynamics and bifurcations of random dynamical systems
  • 14/06/2017: Universität Bielefeld: Workshop on Random Dynamical Systems: Quasi-stationary dynamics and bifurcations of random dynamical systems
  • 26/04/2017: Kyoto Dynamics Days: Random Dynamical Systems Theory and its Applications: Quasi-stationary dynamics and bifurcations of random dynamical systems
  • 16/03/2017: Workshop on Aspects of Dynamical Systems, Imperial College London: Bifurcation Analysis of a Stochastically Driven Limit Cycle
  • 20/10/2016: Goethe-Universität Frankfurt, Analysis Oberseminar: Hopf Bifurcation and Stochastically Driven Limit Cycles
  • 17/10/2016: TU Munich, Dynamical Systems Oberseminar: Hopf Bifurcation and Stochastically Driven Limit Cycles
  • 07/09/2016: Critical Transitions in Complex Systems: Mathematical Theory and Applications, Kulhuse (Denmark): Bifurcation Analysis of a Stochastically Driven Limit Cycle
  • 13/07/2016: 13th International Seminar on Differential Equations, Dynamical Systems and Applications, Isfahan University of Technology: Synchronisation and Chaos for a Stochastically Driven Limit Cycle
  • 18/02/2016 Loughborough University, Stochastic Analysis Seminar: Synchronisation and Chaos in Stochastic Hopf Bifurcation
  • 14/07/2015 Universität Bremen, Dynamical Systems and Geometry Oberseminar: Hopf Bifurcation and Additive White Noise
  • 09/07/2015: Workshop on Random Dynamical Systems and Ergodicity, Loughborough: Hopf Bifurcation and Additive White Noise

Teaching

  • Summer Term 2017: Revision classes for "Applied Functional Analysis" and "Advanced Topics in PDEs"
  • Spring Term 2017: GTA for "Advanced Topics in PDEs"
  • Autumn Term 2016: GTA for "Applied Functional Analysis"
  • Spring Term 2016: GTA for "Ordinary Differential Equations"
  • Spring Term 2016: GTA for "Advanced Topics in PDEs"
  • Autumn Term 2015: GTA for "Dynamical Systems"
  • Autumn Term 2015: GTA for "Applied Functional Analysis"
  • Spring Term 2015: GTA for "Advanced Topics in PDEs"
  • Autumn Term 2014: GTA for "Applied Functional Analysis"
  • Autumn Term 2014: GTA for "Real Analysis"

Awards and Scholarships

  • Since 12/2016: Aligned Student to the Centre for Doctoral Training in the Mathematics of the Planet Earth, Imperial College London and University of Reading
  • Since 2014: Roth Scholarship, Imperial College London
  • 2011-2013: Scholar of the "Max-Weber-Programm Bayern"
  • 2008-2014: Scholar of the "German Scholarship Foundation" (Studienstiftung des Deutschen Volkes)