The main research topics  
The research topics investigated are in real and functional analysis, calculus of variations and PDEs.  
The main themes in real analysis are continuity and related questions, lower semicontinuity, quasi-continuity and its generalizations.  
The main themes in functional analysis deal with the Geometry of Banach Spaces, especially regarding the estimations of the retraction constant, the study of medians and Chebyshev centers, and the theory of fixed points of contractive mappings; moreover, also Sobolev and BV spaces in general metric measure spaces are studied, as well as some topics in Operator Theory.  
The research in calculus of variations mainly focuses on optimal transport and its applications (and interactions with machine learning, see also MaLGa) and geometric measure theory.  
Finally, we are interested in studying the theory of PDEs, including regularity theory for Maxwell’s equations, geometrical and variational aspects of evolutionary PDEs, as well as more applied aspects mainly regarding inverse problems for PDEs such as Calderon’s problem of electrical impedance tomography.