Ben Moonen, Universita'di Nijmegen
On the Tate and Mumford-Tate conjectures for varieties with h^{2,0}=1
Mercoledì 06 Aprile 2016, ore 17:00
Sala di rappresentanza, Dipartimento di Matematica, Università degli Studi, Via C. Saldini 50 | |
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Enzo Mitidieri, Università degli Studi di Trieste
Liouville Theorems in PDE’s: old and new
Martedì 15 Marzo 2016, ore 16:30
Sala Consiglio, 7 piano, Dipartimento di Matematica, Via Bonardi 9, Milano | |
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Camillo De Lellis, Universitaet Zuerich
Regularity and singularity of area-minimizing surfaces
Venerdì 26 Febbraio 2016, ore 11:00
Sala Consiglio, 7 piano, Dipartimento di Matematica, Via Bonardi 9, Milano |
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Abstract
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The Plateau's problem, named after the Belgian physicist J. Plateau, is a classic in the calculus of variations and regards minimizing the area among all surfaces spanning a given contour. A successful existence theory, that of integral currents, was developed by De Giorgi in the case
of hypersurfaces in the fifties and by Federer and Fleming in the general case in the sixties.
When dealing with hypersurfaces, the minimizers found in this way are rather regular: the corresponding regularity theory has been the achievement of several mathematicians in the 60es,70es and 80es (De Giorgi, Fleming, Almgren, Simons, Bombieri, Giusti, Simon among others).
In codimension higher than one, a phenomenon which is absent for hypersurfaces, namely that of branching, causes very serious problems: a famous theorem of Wirtinger and Federer shows that any holomorphic subvariety in $\mathbb C^n$ is indeed an area-minimizing current. A celebrated monograph of Almgren solved the issue at the beginning of the 80es, proving that the singular set of a general area-minimizing (integral) current has (real) codimension at least 2.
However, his original (typewritten) manuscript was more than 1700 pages long. In a recent series of works with Emanuele Spadaro we have given a substantially shorter and simpler version of Almgren's theory, building upon large portions of his program but also bringing some new ideas from partial differential equations, metric analysis and metric geometry. |
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Sir Michael Berry, H H Wills Physics Laboratory, Bristol, UK
Divergent series: from Thomas Bayes’s bewilderment to today’s resurgence via the rainbow
Mercoledì 24 Febbraio 2016, ore 17:00
Sala Consiglio, 7 piano, Dipartimento di Matematica, Via Bonardi 9, Milano | |
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