Anno 2025
 | Seminario Matematico e Fisico di Milano |
| Armen Shirikyan
University of Cergy-Pontoise
Gallavotti–Cohen fluctuation theorem: Universal law of non-equilibrium statistical mechanics.
Mercoledì 26 Febbraio 2025, ore 16:00 precise
Aula seminari MOX, sesto piano del Dipartimento di Matematica, Edificio 14 "La Nave", Politecnico di Milano | |
|
| Seminario Matematico e Fisico di Milano |
| Camillo de Lellis
IAS Princeton
Area-minimimizing currents mod an integer
Martedì 25 Febbraio 2025, ore 14:30 precise
Aula C04, via Mangiagalli 25 |
|
|
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 $\mathbb Z_p$. 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. |
|
|
|
|
|
