[CvGmt News] [Notiziario] [Settimanale] avvisi di seminari

[Giulia Curciarello]

mercoledi' 16-02-2005 (16:00) - Aula Magna
Renling Jin (Charleston, U.S.A) :
Colloquium Dipartimento di Matematica :Magic of Infinitely Large Integers



In a nonstandard model we have many
integers, which are greater than all known positive integers in our standard
world. Are these integers purely for a mind game or useful tools for
understanding our standard world of numbers? In the talk, the
speaker will present some of his results that illustrate how these
infinitely large integers are used for obtaining
new standard theorems in combinatorial number theory. For example, he
recently derived a theorem on Freiman's inverse problems that if A+A is
small, then A must have some arithmetic structure. Freiman's inverse
problems have been popular research topics in combinatorial number theory
since 1960s. The theorem characterizes the arithmetic structure of A
when the size of A+A is 3 times the size of A plus b, where b can be, for
example, any constant integer independent  of the size of A. The best
results before
the speaker's work had been for b < -1.
The audience will not be assumed to have prior knowledge of nonstandard
models. Any people
above undergraduate math level should be able to understand the questions
and theorems without difficulty.


mercoledi' 16-02-2005 (18:00) - Sala delle Riunioni
Antonio Siconolfi (Roma I) :
Seminari di calcolo delle variazioni -Aubry set and applications



For a given Hamiltonian H(x,p) continuous and quasiconvex in the second
argument, defined in RN *RN or on the cotangent bundle of a compact
boundaryless  manifold, we consider the equation H = c with c critical
value,    i.e.   for  which  the  equation  admits  locally
Lipschitz-continuous  a.e.  subsolutions, but not strict subsolutions.
We  show  that  there  is a subset of the state variable space, called
Aubry  set  and denoted by  \A, where the obstruction to the existence of
such subsolution is concentrated. We give a metric characterization
of  \A,  and  we  discuss  its  main properties. They are applied to a
projection  problem  in a Banach space, to the study of the large-time
behavior of subsolutions to a time-dependent Hamilton-Jacobi equation,and
to  construct a Lyapunov function for a perturbed dynamics, under suitable
stability assumptions.

giovedi' 17-02-2005 (15:00) - Sala Seminari
V. Kharlamov (Strasbourg)) :
Logarithmic asymptotics of Welschinger and Gromov-Witten invariants

Argomento: Geometria

For toric Del-Pezzo surfaces, one shows the existence of
real solutions for the problem
of interpolating real points by real rational curves, and we establish
the logarithmic equivalence between
the number of real solutions and the number of complex ones.
We will discuss also the logarithmic asymptotics of genus-0
 Gromov-Witten invariants


Giulia Curciarello
Segreteria Didattica
tel: 050-2213219
e-mail curciare at dm.unipi.it

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