My research area are multidimemsional inverse problems, related topics of analysis and differential geometry, and applications.

Inverse problems tend to identify properties of the model, like coeeficients of the differential equations describing the model, boundaries between subregions within the domaoin of interest which are occupied by different materials, sometimes the shape of the domain itself, etc, when the direct measurements are impossible. This happens in numerous applications: from geophysics to medical imaging, from cosmology to financial market. However, measuring, outside the domain, parameters of various fields penetrating the domain and intercting with material there according to the governing equations of the model, we obtain information, inverse data, which we use to identify the properties of interest.

Depending on whether we deal with a problem in the frequency- or time-domain, these measure data typically correspond to some global characteristics of the model, e.g. spectral properties of the model, or metric proprties, e.g. the travel time between different points on the boundary of the domain. These bring inverse problems into the realm of analysis (spectral theory, PDE-control, etc) and/or differential geometry (metric geometry, comparison geometry, etc). It is not unusual for inverse problems that the type of questions to be answered
if different from the classical ones,provoking new research in these fields.