Research

I am interested in mathematics applied to physics and other sciences.  I am working on open systems---systems exchanging energy with the environment. I use stochastic differential equations (SDE) to model classical open systems.  Quantum open systems are described by master equations or by quantum SDE.  In recent years, the focus of my work was on the small mass limit and noise-induced drift in open systems.  I am also interested on modeling systems which respond to the environment with a time delay.  Such systems are naturally modeled by stochastic differential delay equations (SDDE) and display a range of interesting phenomena.  I also continue working on mathematical problems of the theory of disordered systems and explore applications of mathematics in life sciences---in modeling gene expression and neural circuits.

Most of my work is done in collaboration with physics groups or motivated by such collaboration.  Since 2005 I have been working with the group of Maciej Lewenstein at the Institute of Photonic Sciences (ICFO) in Castelldefels, Spain, on problems in theoretical and mathematical physics.  My collaboration with experimental physicist Giovanni Volpe (currently at the University of Gothenburg, Sweden) and his coworkers dates back to 2008.  It is focused on classical diffusive systems, including systems with sensorial delay.