Il seminario di geometria di questa settimana si terrà Giovedì 9 Maggio alle 16.00 in Aula Seminari. Peter Smillie (Universität Heidelberg) parlerà di "Big minimal surfaces in symmetric spaces". Di seguito l'abstract.

A well-known collection of problems in differential geometry reduce to the study of minimal surfaces in Riemannian symmetric spaces of non-compact type. In general, the derivative of the inclusion of a minimal surface is a holomorphic section of a certain vector bundle — what is special about symmetric spaces is that one can often recreate the minimal surface from this holomorphic data, through what is called the non-Abelian Hodge correspondence. This often lets you describe the moduli space of all minimal surfaces in an interesting way.
However, this process of recreating the minimal surface still involves solving an elliptic PDE, and so precise questions require elliptic
estimates. In this talk, I will try to describe the idea behind the basic interior estimate of Mochizuki and Simpson and some of its
applications, and also tell you about a new version of this estimate with weaker hypotheses and weaker conclusions. This is work in progress with Nathanial Sagman.

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