I am a third year Ph.D. student at SISSA, in the Geometry and Mathematical Physics programme. My doctoral advisors are Antonio Lerario and Paolo Antonini. I have been a part of the Research Group in Real Geometry since September 2024. I am an organizer of the Junior GMP Seminars at SISSA.
You can find my CV here.Â
You can contact me at lbarbato [at] sissa.it
Following the steps of my advisors Antonio Lerario and Paolo Antonini, I am currently studying the metric and topological properties of parameter spaces of geometric (algebraic) objects: given a meaningful embedding, if it exists, of such spaces into a Wasserstein space of probability measures, one studies the induced inner distance. The aim is to have insight on the algebraic parametrized objects and their deformations, through the lenses of differential geometry, symplectic geometry and optimal transport. My field of work is thus metric algebraic geometry, but I am also curious about symplectic topology. Feel free to contact me for more details or to discuss about Mathematics.