Research Interests

Inverse problems are concerned with finding the unknown causes of observed effects. This includes finding the internal structure of an object from external measurements, as in Computerized Tomography and many medical imaging applications, or the parameter values for systems of linear and linear equations that are best aligned with the observed output.

The brain is a complex organ with a variety of functions. My interests in brain modeling span a rather wide range that includes its metabolism, hemodynamics and electrophysiology, and their mutual interactions. There are several mathematical and computational challenges in brain modeling arising from the differences in spatial and temporal scale of its physiological functions

Uncertainty is naturally modeled in probabilistic terms, and while we obviously do not know quantities that we try to estimate, we often have some expectations about them. Bayesian inference is the natural setting for expressing our combination of uncertainty and a priori belief. A large portion of my research combines Bayesian inference and scientific computing.

In the early part of 2020 the COVID-19 pandemic started to change radically structure of social interaction is nearly every country in the world. Mathematical models have been used to study the spread of the infection, predict where the new hotspots would be, assess how effective mitigation measure are and estimate the toll of the pandemic in terms of hospitalizations and deaths. In the wave of COVID-19, I started working with a group of colleagues on predictive model of its spread and management.