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NOTIZIARIO DEI SEMINARI DI ROMA - Settimana dal 2 all'8 luglio 2012

2012-07-02

Seminari di Matematica dell'area romana

Lunedì 2 luglio 2012 
Ore 13:30, Aula di Consiglio 
Seminario di Analisi Matematica 
Benjamin Texier (Università di Parigi VII) 
From Newton to Boltzmann: the case of short-range potentials 
Following Lanford, King, Cercignani-Illner-Pulvirenti, Cercignani-Gerasimenko-Petrina, and Esposito-Pulvirenti, we give a rigorous derivation of the Boltzmann equation as the mesoscopic limit of systems of Newtonian particles interacting via a short-range potential, as the number of particles N goes to infinity and the characteristic size of the particles epsilon simultaneously goes to 0, in the Boltzmann-Grad scaling N epsilon^[d-1] = 1. This is joint work with Isabelle Gallagher and Laure Saint-Raymond.
Martedì 3 luglio 2012 
Ore 12:30, Aula 1B1, Dipartimento SBAI 
Barbara Prinari (Università di Lecce) 
Coupled Maxwell-Bloch equations with inhomogeneous broadening for a 3-level system 
The phenomenon that describes the effect of a coherent medium response to an incident electric field, to which the medium is totally transparent and which undergoes lossless propagation, is known as self-induced transparency (SIT). SIT was first discovered by McCall and Hahn (1969) in the case of non-degenerate two-level atoms. Special solutions for the two-level system were found by Lamb (1971), while the initial value problem for the propagation of a pulse through a resonant two-level optical medium was solved by Inverse Scattering Transform (IST). It is possible to formulate the SIT equations in the framework of the IST also in the case of a three-level system. While the associated scattering problem is the same as for the coupled nonlinear Schroedinger equation, the time evolution depends on asymptotic values of the material polarizability envelopes and is highly non-trivial. This talk will address the solution of the initial value problem for the SIT equations for three level systems, for generic preparation of the medium, and describe its soliton interactions.
Mercoledì 4 luglio 2012 
Ore 14:30, Aula di Consiglio 
Seminario di Algebra e Geometria 
Ping Xu (Penn State University) 
Atiyah classes and homotopy algebras 
The Atiyah class of a holomorphic vector bundle is the obstruction class to the existence of a holomorphic connection on the holomorphic vector bundle. It is a classical theorem of Kapranov that for a complex manifold X, the Atiyah class of TX makes TX[-1] into a Lie algebra object in the derived category D^+(X). Moreover, Kapranov proved that for any Kaehler manifold X, such a Lie algebra structure is indeed induced from an L^infty algebra structure on Omega^[0,*-1](TX). Kapranov theory played a fundamental role in understanding Rozansky-Witten theory, and has recently inspired many active research in deformation quantization theory. In this talk, we will show how Kapranov theorems can be extended to a general setting of the so called Lie pair, i.e. a Lie algebroid together with a Lie subalgebroid. In this way, we obtain many new homotopy algebras.

Tutte le informazioni relative a questo notiziario devono pervenire all'indirizzo di posta elettronicaseminari@mat.uniroma1.it, o nella casella della posta di Luigi Orsina, entro le ore 9 del venerdì precedente la settimana di pubblicazione. 

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