Variational methods and symmetric orbits for the n-body problem.
Abstract: Periodic and quasi-periodic orbits for the $n$-body problem can
be found as critical points of the action functional constrained to the space of
equivariant loops. Without strong-force assumptions, existence and properties of
symmetric collisionless (quasi-)periodic orbits can be proved to exist by
such equivariant variational methods, provided the
symmetry group fulfills
some simple assumptions. As a consequence, global and local optimization
numerical techniques can be used to determine and visualize approximations of
such periodic orbits.
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giovedi' 23-03-2006 (11:00) - Sala Seminari
Carlo Traverso (Dip.
di Matematica - Pisa) :
INTRODUZIONE AI METODI ARITMETICI DELLA
CRITTOGRAFIA
Argomenti:
Generalità sulla crittografia a chiave pubblica.
Protocolli
RSA e Diffie-Hellmann.
Algoritmi per la fattorizzazione:
rho di Pollard, p-1 di Pollard,crivello quadratico.
Algoritmi per il
logaritmo discreto: baby step-giant step, rho di Pollard, Pohlig-Hellmann, index
calculus.
Curve ellittiche: fattorizzazione con curve
ellittiche,
Diffie-Hellmann su curve ellittiche.
Il corso
consisterà in (presumibilmente) tre seminari di 90 minuti. L'orario successivo
sarà deciso nella prima riunione (la seconda sarà probabilmente venerdì 24 alle
12 ma non si escludono cambiamenti).
E' possibile che vi sia una
seconda serie di seminari con argomenti più avanzati (number field sieve,
conteggio dei punti delle curve ellittiche, algoritmi per il logaritmo discreto
sulle curve ellittiche, crittografia iperellittica) con inviti di
specialisti.
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venerdi' 24-03-2006 (16:00) - Sala Riunioni
Petar Popivanov
(Institute of Mathematics, Bulgarian Academy of Sciences Bulgaria) :
Local properties of the solutions and
characteristic Dirichlet problem for a class of degenerate parabolic
operators
seminario PDE
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mercoledi' 29-03-2006 (24:00) - 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.
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