Davide Parise (Imperial) will give the geometry seminar at 2pm on 8th December, in Salle des Profs, 9th floor of building NO. Davide’s title is “Log-epiperimetric inequalities for conformally invariant geometric variational problems” and his abstract is below.
Log-epiperimetric inequalities were introduced in seminal work of Reifenberg to study solutions of the Plateau problem, and have since played a fundamental role in understanding the regularity of solutions to various variational problems, including minimal submanifolds and free boundary problems. In this talk, I will introduce this technique and discuss how it can be adapted to the setting of two famous conformally invariant geometric varitional problems: the Yang-Mills functional, a celebrated Lagrangian central to the development of 4-manifolds geometry, and harmonic maps, the nonlinear generalisation of harmonic functions. Furthermore, I will explain how to establish uniqueness of blow-ups with isolated singularities. This is based on joint works with Riccardo Caniato.