I am a Research Fellow in Applied Mathematics at the University of Auckland, specialising in dynamical systems, chaos and bifurcation theory. My research focuses on a higher-dimensional type of chaos called “wild chaos”. My research aims to find the geometric mechanisms that generate this abstract type of chaos in explicit systems. Moreover, I study how this type of chaos can be identified in applications by developing advanced numerical methods for the computation of invariant sets (such as stable and unstable manifolds) and the identification and continuation of their bifurcations. This type of dynamics can appear in noninvertible maps of dimension at least two, diffeomorphisms of dimension at least three and vector fields of dimension at least four.

Biography

After finishing my Diploma degree in Mathematics at Bielefeld University (Germany) in 2009, I started my PhD at the University of Bristol (UK) with Hinke Osinga and Bernd Krauskopf in 2010. Together with my supervisors I transferred to the University of Auckland in 2011, where I completed my PhD thesis in 2013. My name was put on the Graduate Dean’s list of excellent doctoral theses and I was suggested for the Vice Chancellors Best Thesis Award in 2014. Furthermore my PhD research was recognised by the Aitken Prize for the best student talk at the New Zealand Mathematical Society Colloquium 2012. I started my current position as a Research Fellow in Applied Mathematics at the University of Auckland in 2014. In addition to my research, I have been a lecturer for the courses “Differential Equations” (Maths260), “Great Ideas Shaping our World” (Maths190) and “Numerical Computation” (Maths270).

Research Interests

  • Higher-dimensional chaos: wild chaos, heterodimensional cycles, blenders
  • Lorenz-like systems and their global invariant manifolds
  • Bifurcations of noninvertible maps
  • Generalised Julia and Mandelbrot sets in nonanalytic maps
  • The Allee effect in predator-prey dynamics
  • Inverse limits in set-valued Lorenz maps