Camillo de Lellis, IAS Princeton
Area-minimimizing currents mod an integer
Martedì 25 Febbraio 2025, ore 14:30 precise
Aula C04, via Mangiagalli 25 |
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Abstract
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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. |
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Andrea Mondino, University of Oxford
Smooth and non-smooth aspects of Ricci curvature lower bounds
Mercoledì 02 Ottobre 2024, ore 16:00 precise
Sala del Consiglio (piano 7) | |
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Enrico Valdinoci, University of Western Australia
Nonlocal minimal surfaces: regularity, stickiness, sheeting phenomena
Venerdì 21 Giugno 2024, ore 11:00 precise
Sala Consiglio, settimo piano, Dipartimento di Matematica, Edificio 14 "La Nave", Politecnico di Milano | |
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Jaqueline Godoy Mesquita, University of Brasilia
Averaging principles and stability in the context of functional differential equations
Lunedì 17 Giugno 2024, ore 15:15
Sala Consiglio, settimo piano, Dipartimento di Matematica, Edificio 14 "La Nave", Politecnico di Milano | |
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Dan Virgil Voiculescu, Department of Mathematics, University of California, Berkeley
On the Many Faces of the Quasicentral Modulus: from Perturbations of Operators to Noncommutative Condensers
Lunedì 10 Giugno 2024, ore 16:30 precise
Sala Consiglio, settimo piano, Dipartimento di Matematica, Edificio 14 "La Nave", Politecnico di Milano | |
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Abbas Moameni, Carleton University, Ottawa
Stratified Monge-Kantorovich optimal transport problems, structure and the uniqueness of optimal transport plans.
Lunedì 06 Maggio 2024, ore 16:30
Aula seminari MOX, sesto piano, Dipartimento di Matematica, Politecnico di Milano | |
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