Martedì 25 febbraio 2025, ore 14.30,
presso Aula C04, via Mangiagalli 25, Università di Milano,
nell'ambito delle iniziative del Seminario Matematico e Fisico di Milano,
si svolgerà il seguente seminario:
Titolo. Area-minimimizing currents mod an integer.
Autore. Camillo de Lellis, IAS Princeton
Abstract. Currents mod p are a suitable generalization of classical chains mod p, i.e. of finite combinations of smooth submanifolds with coefficients in the cyclic group Zp. By the pioneering work of Federer and Fleming it is possible to minimize the area in this context and, for instance, represent mod p homology classes with area minimizers. For p>2 typically (i.e. away froma small set of exceptional points) one would expect such minimizers to be a union of smooth minimal surfaces joining together (in multiples of p's'') at some common boundary. This is however surprisingly challenging to prove, especially for even p's, and up until recently only known for p=3 and 4 in codimension 1. In this talk I will explain the outcome of a series of more recent works (some joint of the speaker with Hirsch, Marchese, Stuvard and Spolaor, some by Wickramasekera and Minter-Wickramasekera, and some joint of the speaker with Minter and Skorobogatova) which confirms this picture, with varying degrees of precision in a variety of situations.