Our current research is centered around operator-theoretic approach to analysis of nonlinear dynamical systems, applications in microfluidics and (bio)-nanotechnology. The research topics can be grouped as follows:

  • Mixing and separation in fluids across the scales with applications ranging from microfluidic phenomena to oceanographic flows,
  • Nano and micro-scale particle dynamics induced by dielectrophoresis and otherelectrokinetic phenomena, with applications to biotechnology,
  • Multiscale dynamics of the Atomic Force Microscope, including interactions with biomolecules,
  • Dynamical systems theory of complex systems, including large-scale networked systems

In each of these topics, the research is characterized by pursuit of the key physical phenomena in a device or system followed by the abstraction of the mathematical problem (or problems) associated with it. We close the loop by applying the solution of the mathematical problem to explain the physical phenomena or design new concepts based on which devices can be built or improved.

News

3/31/2017- Igor Mezic elected SIAM fellow!

This week, the Society for Industrial and Applied Mathematics (SIAM) announced the class of 2017 SIAM fellows. This fellowship "honors SIAM members who are recognized by their peers as distinguished for their contributions to the discipline". Igor Mezic was elected among ~30 other applied mathematicians for his sustained innovation at the dynamical systems theory/applications interface; notably for advances in the use of Koopman operator theory...

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09/15/2016 - 09/16/2016

Professor Takashi Hikihara from University of Tokyo is visiting the Mezic Research Group Thursday and Friday.

08/31/2016 - Accepted Manuscript "Programmable Potentials: Approximate N-body potentials from coarse-level logic"

Our manuscript "Programmable Potentials: Approximate N-body potentials via coarse-level logic", co-authored by Gunjan Thakur, Ryan Mohr, and Igor Mezic, has been accepted for publications by Scientific Reports.

06/30/2016 - Oberwolfach report released for Applied Koopmanism mini-workshop

Mathematisches Forschungsinstitut Oberwolfach has released the preliminary report for our mini-workshop "Applied Koopmanism", held at the institue February 7 - 13. The workshop focused on the interplay of ergodic theory, operator theory, geometric dynamical systems and convex optimization methods in pure and applied contexts. It was organized by Igor Mezic, Mihai Putinar (UCSB, Mathematics), and... Read more