Antonia Diana
University of Trento
University of Trento
I am currently a Postdoctoral Researcher in Mathematical Analysis at the Department of Mathematics of Univeristy of Trento, in the research group of Prof. Andrea Marchese. This position is founded by the FIS_2 CoG: SingMeas grant.
Previously, I was a Postdoctoral Researcher at Sapienza University of Rome where I collaborated with Prof. Marcello Ponsiglione.
I obtained my PhD at the Scuola Superiore Meridionale under the supervision of Carlo Mantegazza and Alessandra Pluda.
My research lies at the intersection of geometric analysis, geometric measure theory, calculus of variations and partial differential equations. It is mainly focused on the study of geometric flows and their interplay with variational problems.
Over the past years, I have worked on:
Nonlocal geometric flows arising as gradient flows of generalized perimeters, with a discrete-in-time analysis via minimizing movements;
Surface diffusion flow and related higher-order geometric evolutions, including global existence, asymptotic stability, and regularity theories valid in arbitrary dimensions;
Elastic flows of curves, including boundary effects and higher-order energies, with emphasis on existence, stability, and long-time behavior through analytic and variational techniques.