Seminari di Fisica Matematica
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| Seminari A.A. 2010-2011 |
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Relatore |
Titolo |
Data |
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Francesco Cellarosi
Princeton University |
19 Luglio 2011 |
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Karol Kozlowski
DESY |
30 Giugno 2011 (giovedì) |
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Elena Pulvirenti
Università di Roma Tre |
26 Giugno 2011 (giovedì aula 211) |
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Antonio Di Carlo
Università di Roma Tre |
12 Aprile 2011 |
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Abstract ritorna |
A k-measure on an n-dimensional manifold M (a notion introduced
in a rather old and little-known paper by Fichera) is basically a k-vector
valued measure. Absolutely continuous k-measures may be identified with
locally summable k-vector fields. Any k-submanifold S ⊂ M
(k ≤ n) induces a distinguished k-measure supported by the closure of
S (hence singular, unless k=n). If a k-measure is not too singular,
its boundary is a (k−1)-measure. In particular, the boundary of the k-measure
induced by a k-submanifold with boundary S is the (k−1)-measure induced
by its boundary ∂S. On this basis, I am able to define in a
satisfactory way the boundary of k-measures in terms of Lie derivatives,
dualizing Palais' definition of the exterior derivative. The spaces of
real-valued k-chains and k-cochains are the discrete analogs - or, better,
antecedents - of the spaces of k-measures and k-forms, respectively.
Cochains represent densities with respect to the measures imparted to cells
by chains, and the duality pairing between them is a discrete preliminary
to integration. Measure, however, does not exhaust geometry.
To impart metric properties to the space of chains, one has to endow
it with an inner product. To this end, I associate linearly
an absolutely continuous and square-integrable k-measure on M with each
k-chain, and identify the inner product between two k-chains with the inner
product between the corresponding k-vector fields. This talk is partially
based on joint work with F. Milicchio, A. Paoluzzi, and V. Shapiro. |
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Yuri Kondratiev
Universität Bielefeld |
Kawasaki type dynamics for IPS in continuum |
01 Marzo 2011 |
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Michela Procesi
Università di Napoli "Federico II" |
22 Febbraio 2011 |
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Ioannis Anapolitanos
Toronto University |
11 Febbraio 2011 (venerdì) |
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Kevin Schnelli
ETH Zurich |
08 Febbraio 2011 |
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Daniel Egli
ETH Zurich |
01 Febbraio 2011 |
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Michele Correggi
CIRM Università di Trento |
18 Gennaio 2011 |
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Enrico Valdinoci
Università di Roma "Tor Vergata" |
09 Novembre 2010 |
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Serena Cenatiempo
Università di Roma "La Sapienza" |
02 Novembre 2010 |
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Livia Corsi
Università di Roma Tre |
27 Ottobre 2010 (mercoledì ore 16.00) |
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Eva Löcherbach
Université de Cergy-Pointoise |
05 Ottobre 2010 (ore 15.00) |
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