Gabriella Tarantello, Università di Roma
Sullo Studio dei Vortici di Chern-Simons in contesti Autoduali
Thursday, February 26 2015, at 11:00 precise
Aula Consiglio 7° piano | |
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Antonio Leaci, Università del Salento
Free discontinuity problems and image inpainting
Monday, February 16 2015, at 15:00 precise
Aula Consiglio VII piano | |
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Luigi Accardi, Università di Roma Tor Vergata
LE RADICI CLASSICHE DELLA TEORIA QUANTISTICA
Tuesday, January 27 2015, at 17:00
Università di Milano, Dipartimento di Matematica, Via Saldini 50, Sala di rappresentanza |
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Abstract
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For several decades the mathematical model of Quantum Probability (QP) has been considered as a generalization of classical probability.
However some discoveries of the past 15 years show that the whole quantum theory, including quantum fields, is not a generalization,
but rather a deeper level of classical probability.
In fact, combining classical probability with the theory of
orthogonal polynomials in 1 or several real variables, it is possible to
prove that the canonical commutation relations, both Fermi and Bose
(and in fact even their $q$-deformations), arise canonically from the Bernoulli and Gaussian random variables respectively.
More generally one can prove that there is a one-to-one correspondence between Heisenberg-type commutation relations
and equivalence classes of probability measures on R with all moments.
The equivalence relation being defined, in the one-dimensional case,
by the fact that all measures in a class share the same principal
Jacobi sequence.
To each of these equivalence classes it is canonically associated a
free evolution, generalizing the classical harmonic oscillator evolution.
The characterization of the equilibrium states with respect to any such evolution naturally leads to a generalization of the Planck factor.
Similar arguments, applied to the recently introduced local
equilibrium states, lead to non-linear extensions of the Planck factor and non-linear Gibbs states.
Being functorial, the above construction also provides a generalization
of the second quantization procedure both at Hilbert space (Fock)
and $*$-algebra level and in some special cases (e.g. probability measures
on $R^d$ with compact support) even at $C^*$-algebra level.
However in general the class of morphisms will be much narrower than
in usual second quantization.
This fact supports the intuition that the new quantizations have a physical meaning in terms of non-linear completely integrable classical systems.
The present talk is concentrated on the goal to illustrate
the classical roots of quantum theory, however
if time allows it will be also mentioned how these new ideas have allowed
to solve a multiplicity of long standing open problems both in
classical probability and in the theory of orthogonal polynomials.
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Fabrizio Catanese, Mathematisches Institut, Universitaet Bayreuth
SPAZI DI MODULI DI VARIETA PEROIETTIVE CLASSIFICANTI, E LA AZIONE DEL GRUPPO DI GALOIS ASSOLUTO
Thursday, December 11 2014, at 17:00
Università di Milano, Dipartimento di Matematica | |
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Dorin Bucur, Université de Savoie
SHAPE OPTIMIZATION PROBLEMS WITH ROBIN BOUNDARY CONDITIONS
http://www.lama.univ-savoie.fr/~bucur
Friday, November 07 2014, at 12:00
Politecnico di Milano, Dipartimento di Matematica, Sala Consiglio, piano VII | |
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Dorin Bucur, Université de Savoie
Shape optimization problems with Robin boundary conditions.
Friday, November 07 2014, at 12:00 precise
Politecnico di Milano - Dipartimento di Matematica 7° piano - Sala Consiglio | |
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