COLLOQUIO DE GIORGI
Zeev Rudnick
Tel Aviv University
"Eigenvalue statistics and lattice points"
One of the more challenging problems in spectral theory and mathematical physics today is to understand the statistical distribution of eigenvalues of the Laplacian on a compact manifold.
There are now several challenging conjectures about these, originating in the physics literature.
I will describe what is conjectured and what is known the very simple case of the flat torus, where the problems amount to counting lattice points in annuli and have a definite arithmetic flavour.
Martedì 9 maggio 2006
ore 17.00
Aula Mancini
Piazza dei Cavalieri, 7
PISA
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AVVISO
Il ciclo di seminari di Analisi Armonica, proseguirà
Giovedì 6 aprile alle ore 11.00 in aula Tonelli
sul seguente argomento:
"Nonlinear Schroedinger equation on four-dimensional
compact manifolds"
Vittoria Pierfelice
(Scuola Normale)
Abstract
We prove two new results about the Cauchy problem in the energy space for nonlinear Schroedinger equations on four-dimensional compact manifolds. The first one concerns global wellposedness for Hartree-type nonlinearities and includes approximations of cubic NLS on the sphere. The second one provides, in the case of zonal data on the sphere, local wellposedness for quadratic nonlinearities as well as global wellposedness for small energy data in the Hamiltonian case. Both results are based on new multilinear Strichartz-type estimates for the Schroedinger group.
Il programma dei seminari proseguirà a cadenza settimanale, in aula Tonelli, con lo stesso orario.
Tutti gli interessati sono invitati a partecipare.
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martedi' 04-04-2006 (14:00) - Aula Seminari
Jacky CRESSON (IHES Paris) :
Mould calculus and normalization of vector fields or diffeomorphisms I
SEMINARI DI SISTEMI DINAMICI OLOMORFI (e dintorni)
ABSTRACT
This talks will provide an introduction to mould calculus, as introduced by Jean Ecalle. We shall give a precise definition of moulds and describe their main properties, and we shall apply this formalism to the problem of normal forms for vector fields and iffeomorphisms.
**********************************************************************
mercoledi' 05-04-2006 (14:00) - Centro "De Giorgi"
Jacky CRESSON (IHES Paris) :
Mould calculus and normalization of vector fields or diffeomorphisms
SEMINARI DI SISTEMI DINAMICI OLOMORFI (e dintorni)
ABSTRACT
This talks will provide an introduction to mould calculus, as introduced by Jean Ecalle. We shall give a precise definition of moulds and describe their main properties, and we shall apply this formalism to the problem of normal forms for vector fields and diffeomorphisms.
**********************************************************************
mercoledi' 05-04-2006 (16:00) - Sala delle Riunioni
Jeffrey Rauch (University of Michigan) :
A Transmission Strategy for Hyperbolic Internal Waves of Small Width
Argomento: Analisi
Abstract:
Semilinear hyperbolic problems with
source terms piecewise smooth and discontinuous across characteristic surfaces yield similarly piecewise smooth solutions. If the discontinuous source is replaced with a smooth transition layer, the discontinuity of the solution is replaced by a smooth internal layer. In this paper we describe how the layer structure of the solution can be computed from the layer structure of the source in the limit of thin layers. The key idea is to use a transmission problem strategy for the problem with the smooth internal layer. That leads to an ansatz different from the obvious candidates. The obvious candidates lead to overdetermined equations for correctors. With the transmission problem strategy we compute infinitely accurate expansions.
***********************************
Segreteria Didattica
Giulia Curciarello
tel- 050 2213219
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>
> CENTRO DI RICERCA MATEMATICA ENNIO DE GIORGI
>
> 'Stochastic Partial Differential Equations'
> 3-7 Aprile, 2006
>
> All'indirizzo
>
> http://www.crm.sns.it/workshopaprile.html
>
> si trova il calendario aggiornato del workshop 'Stochastic Partial
> Differential Equations', che si terra' dal 3 al 7 Aprile, nell'ambito
> del semestre su 'Stochastic Analysis, Stochastic PDEs and Applications
> to Fluid Dynamics and Particle Systems' (cfr. www.crm.sns.it).
>
> Tutti gli interessati sono invitati a partecipare.
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SEMINARIO DI MATEMATICA
Giovedì 30 marzo 2006
ore 14.30
Scuola Normale Superiore
Pisa
(Aula Bianchi)
NIKOLAY KRUZHILIN
Steklov Mathematical Institute
Russian Academy of Sciences, Moscow
Terrà un seminario dal titolo:
"MAPS OF REINHARDT DOMAINS"
Tutti gli interessati sono invitati a partecipare.
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martedi' 28-03-2006 (04:00) - Dipartimento di Matematica Applicata Via Bonanno Pisano 25/b
Daniela Visetti (University College Cork, Irlanda) :
Homoclinic trajectories and chaotic behaviour for a piecewise linear oscillator
Abstract:
Consideriamo l'equazione $\ddot x + x = \sin(\sqrt{2}t)+s(x)$ con $s(x)$ limitata, lineare a tratti e il sistema dinamico associato all'operatore di shift lungo le traiettorie di un tempo $\sqrt{2}\pi$ (il periodo del
termine forzante). Dimostriamo l'esistenza di comportamento caotico su un sottoinsieme dell'area di instabilità di Mather. La dimostrazione è computer-assisted e utilizza tecniche di grado topologico (del tipo di Zgliczynski e di Pokrovskii).
Segreteria Didattica
Giulia Curciarello
tel- 050 2213219
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mercoledi' 29-03-2006 (04:00) - Dipartimento di Matematica Applicata Via Bonanno Pisano 25/b
Daniela Visetti (University College Cork, Irlanda) :
Homoclinic trajectories and chaotic behaviour for a piecewise linear oscillator
Abstract:
Consideriamo l'equazione $\ddot x + x = \sin(\sqrt{2}t)+s(x)$ con $s(x)$ limitata, lineare a tratti e il sistema dinamico associato all'operatore di shift lungo le traiettorie di un tempo $\sqrt{2}\pi$ (il periodo del
termine forzante). Dimostriamo l'esistenza di comportamento caotico su un sottoinsieme dell'area di instabilità di Mather. La dimostrazione è computer-assisted e utilizza tecniche di grado topologico (del tipo di Zgliczynski e di Pokrovskii).
Segreteria Didattica
Giulia Curciarello
tel- 050 2213219
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mercoledi' 29-03-2006 (15:30) - Sala Seminari
Priska Jahnke (Bayreuth) :
Terminal Fano threefolds and their smoothings
Argomento: Geometria
Abstract:
Let X be a Gorenstein Fano threefold with at most canonical singularities. It is known, that there are only finitely many deformation families of such X, so one may ask for a complete classification as was done in thesmooth case by Iskovskikh, Mori and Mukai. An important question is under which conditions X arises as a degeneration of a smooth Fano threefold, and if that is the case, how X and its "smoothing" are related. In 1997 Namikawa proved the existence of a smoothing, if X has only terminal singularities, i.e., X is the special fiber of a flat family Z -> D with general fiber Z_t a smooth Fano threefold. Here Z is an irreducible complex space, not necessarily smooth. We show that the Picard groups of X and Z_t are isomorphic in the terminal case and give some examples concerning canonical singularities. Here a smoothing need notexist, and even if it exists, the Picard number may jump.
Segreteria Didattica
Giulia Curciarello
tel- 050 2213219
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> CENTRO DI RICERCA MATEMATICA ENNIO DE GIORGI
>
> Nell'ambito del semestre su 'Stochastic Analysis, Stochastic PDEs and
> Applications to Fluid Dynamics and Particle Systems' (cfr.
> www.crm.sns.it), dal 3 al 7 Aprile prossimi si terra' un workshop dal
> titolo:
>
> 'Stochastic Partial Differential Equations'
>
> Le lezioni si terranno in Aula Dini (Via del Castelletto, 11).
>
> Il calendario delle lezioni, con i relativi abstracts, e' reperibile
> all'indirizzo:
>
> http://www.crm.sns.it/workshopaprile.html
>
> Tutti gli interessati sono invitati a partecipare.
>
>
> --
> Ilaria Gabbani
> Centro di Ricerca Matematica Ennio De Giorgi
> Collegio Puteano, Scuola Normale Superiore
> Piazza dei Cavalieri, 3
> I-56100 PISA
>
> Phone: ++39-050-509178
> Fax: ++39-050-509177
>
> e-mail: crm(a)crm.sns.it
> http://www.crm.sns.it
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