My work is in dynamical systems and its applications.
Many natural and engineered systems operate across multiple time scales. I study geometric mechanisms underlying abrupt transitions, delayed loss of stability, and multiscale instabilities, with an emphasis on global phase-space structure.
Keywords: geometric singular perturbation theory, canards, critical transitions, multiscale bifurcations
I use ideas and techniques from singularity and bifurcation theory to analyze degenerate structures that organize the dynamics of differential equations. Many slow–fast systems exhibit non-hyperbolic points where classical perturbation theory breaks down. These degeneracies act as organizing centers for global bifurcations and phase-space geometry.
A central theme of my work is the systematic desingularization of such points via blow-up and related geometric techniques. This transforms non-generic configurations into higher-dimensional but regular systems where invariant manifolds, stability, and bifurcation mechanisms can be studied with standard tools. This ultimately yields precise information about the original system and its parameter dependence.
Keywords: geometric desingularization, blow-up methods, non-hyperbolic singularities, slow–fast systems
Many realistic models consist of subsystems coupled through a network. I study how network structure constrains and shapes dynamics, especially when interactions occur across multiple time or organizational scales. A particular focus is on adaptive and higher-order network effects, and how they modify collective behavior and the validity of classical reduction methods.
Keywords: adaptive networks, higher-order coupling, multiscale dynamics, network singularities
I enjoy collaborations with researchers in (applied) mathematics, control theory, mathematical neuroscience, engineering, (systems) biology, chemistry, etc. especially where a model suggests a clear mathematical question.
For a full publication list, see the Publications page.