Notiziario Scientifico
Notiziario dei Seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 19 al 25 ottobre 2015
Lunedì 19 ottobre 2015
Ore 14:30, aula di Consiglio
Seminario di Analisi Matematica
Alexandre Boritchev (Université Claude Bernard Lyon)
Hyperbolicity of the minimizers for the stochastic Burgers equation
We consider the stochastic Burgers equation from a Lagrangian viewpoint.
In other words, we study the dynamical behaviour of the energy minimisers
which give the variational behaviour of the solution. Under non-degeneracy
assumptions on the random forcing, we prove hyperbolicity of these minimisers,
considerably simplifying the proof in [E, Khanin, Mazel, Sinai, Annals, 2000].
Finally, we will speak about the relationship between this problem and the
convergence to the stationary measure for the solutions of the equations.
This is a joint work with K. Khanin (Toronto).
Lunedì 19 ottobre 2015
Ore 15:30, aula B
Seminario di Storia e Didattica della Matematica
Claudio Bernardi (Sapienza Università di Roma)
Proprietà inaspettate di grafici di funzioni reali
Lo studio di situazioni insolite, e anzi contrarie alle aspettative, può
avere interesse sia dal punto di vista logico sia nella pratica didattica.
Nel seminario si parlerà di un argomento elementare (funzioni reali
di variabile reale e loro grafici), ma saranno esaminate situazioni diverse
da quelle consuete. Si tratta di casi in cui è difficile 'vedere' gli oggetti
in gioco perché le rappresentazioni usuali sembrano fallire.
In particolare, si parlerà di funzioni periodiche e quasi periodiche,
di funzioni additive discontinue, di funzioni ovunque suriettive. Per la
comprensione del seminario è richiesta solo la conoscenza dei concetti
che si studiano nei corsi di base (in un paio di occasioni sarà applicato
l'assioma di scelta).
Lunedì 19 ottobre 2015
Ore 16:00, aula di Consiglio
Seminario di Probabilità
Paul Chleboun (University of Warwick)
Large deviations of the empirical current in zero-range
processes on a ring
We examine atypical current fluctuations in totally asymmetric
zero-range processes in one dimension with periodic boundary
conditions. The zero-range processes is a stochastic lattice gas
in which each lattice site can be occupied by, a-priori, an unbounded
number of particles. Particles move to their neighbour at a rate which
only depends on the occupation of the departure site. For large
systems, by calculating the Jensen-Varadhan action functional, we are
able to find the time dependent optimal profiles which realise
currents below the typical value. Under certain conditions on the jump
rates, we demonstrate that these systems can exhibit a dynamical phase
transition, in which above a critical non-typically current the
optimal macroscopic density profile is given by a traveling wave with
a shock and anti-shock pair. While rare events below the critical
current are realised by a condensate, whereby a non-zero fraction of
all the particles accumulate on a single site in the thermodynamic
limit. This gives rise to a non-convex rate function for the empirical
current, which in turn leads to a breakdown of the equivalence between
the conditioned dynamics and the s-ensemble cloning methods typically
used in simulations to sample these rare events.
Lunedì 19 ottobre 2015
Ore 16:30, aula Picone
Seminario di divulgazione scientifica per scuole superiori
Luigi Orsina (Sapienza Università di Roma)
Origami e simmetrie
Lunedì 19 ottobre 2015
Ore 17:00, aula di Consiglio
Seminario di Probabilità
Alexandre Boritchev (Université de Lyon)
1D and multi-d Burgers Turbulence as a model case for the
Kolmogorov Theory
The Kolmogorov 1941 theory (K41) is, in a way, the starting point for
all models of turbulence. In particular, K41 and corrections to it
provide estimates of small-scale quantities such as increments and
energy spectrum for a 3D turbulent flow. However, because of the
well-known difficulties involved in studying 3D turbulent flows, there
are no rigorous results confirming or infirming those predictions.
Here, we consider a well-known simplified model for 3D turbulence:
Burgulence, or turbulence for the 1D or multi-dimensional potential
Burgers equation.
In the space-periodic case with a stochastic white in time and smooth in
space forcing term, we give sharp estimates for small-scale quantities
such as increments and energy spectrum.
Martedì 20 ottobre 2015
Ore 15:00, IMATI-CNR, via Ferrata
Colloquium Magenes
Juan Luis Vazquez (Universidad Autónoma de Madrid),
Nonlinear diffusion in theory and applications.
Local and nonlocal models
Martedì 20 ottobre 2015
Ore 15:00, aula G
Seminario per insegnanti (Piano Lauree Scientifiche)
Luigi Orsina (Sapienza Università di Roma)
Origami e polinomi!
Mercoledì 21 ottobre 2015
Ore 14.30, aula di Consiglio
Seminario di Algebra e Geometria
Maxim Kontsevich (IHES)
On microlocal support, Stokes structures and cluster coordinates
Giovedì 22 ottobre 2015
Ore 14:00, aula di Consiglio
Seminario P(n): problemi differenziali non lineari
Italo Capuzzo Dolcetta (Sapienza Università di Roma)
A few recent analitycal and numerical results about the principal
eigenvalue of degenerate elliptic operators
I will report on recent joint papers [1] with Berestycky, Porretta and
Rossi (JMPA 2014) and [2] with Birindelli and Camilli (2015 submitted).
An extended notion of principal eigenvalue is introduced in [1] in the
general framework of fully nonlinear degenerate elliptic operators; the
positivity of this number is shown to be equivalent to the sign
propagation property.
Under stronger ellipticity conditions we proposed in [2] some finite
differences schemes to compute this number. It is worth to point out that
standard numerical approaches to the computation of eigenvalues are based
on the classical Rayleigh-Ritz formula requiring divergence structure of
the operator which is not required in our method.
Venerdì 23 ottobre 2015
Ore 11.00, aula 311, Università di Roma Tre,
largo san L. Murialdo 1
Seminario di Logica e Geometria della Cognizione
Virgile Mogbil (Université Paris XIII)
Proofs as schedules
(Proofs as schedules) is a new approach about the proof-theoretic
study of concurrent interaction. Through the Curry-Howard
correspondence proof theory is well suited to describe confluent
systems. Because the meaning of proofs lies in their normal forms, cut
elimination should be confluent in order to preserve it. On the other
hand concurrency has non-determinism as a fundamental feature. In
process calculi the meaning of a term is not its final irreducible
form but what happens to get there, as interaction with other
processes... hence term reduction i.e. execution of interactions
should definitely not preserve meaning. We propose a correspondence
between proofs in linear logic and interaction plans for processes,
called schedules.
Venerdì 23 ottobre 2015
Ore 12.00, aula di Consiglio
Seminari MoMa
Fabio Pellacini
Appearance Fabrication: An Optimization Approach
Today's 3D printers are likely to revolutionize personal fabrication, with
their hardware improving everyday and their cost getting lower. In this walk,
I will present my work in using 3D printers to replicate the appearance of
objects. I will show that the base of using 3D printers effectively is the
solution of complex optimization problems.
Time permitting, I will also introduce others' work in this area.
Venerdì 23 ottobre 2015
Ore 14.30, aula Grassano, Università di Roma Tor Vergata
Seminario Teorico
Eric Carlen (Rutgers University)
A Quantum Kac Walk and its Kinetic Limit
We present recent results on models for quantum systems of N particles
undergoing random binary collisions, focusing on propagation of chaos and
the rate of convergence to equilibrium. These questions arise from the work
of Mark Kac and his investigation into the probabilistic structure underlying
the Boltzmann equation. Recently, the quantum mechanical variation on Kac's
question has begun to be investigated. In this case, the Kac Master equation
becomes an evolution equation of Lindblad type, while the corresponding
Boltzmann equation is a novel sort of non-linear evolution equation for
a density matrix. There are novel difficulties due to the fact that in
quantum mechanics, conditional probability is not always well-defined.
Nonetheless, a substantial quantum analog of of the Kac program can be
carried out, and this leads to an interesting and novel class of quantum
kinetic equations. This is joint work with Michael Loss and Maria Carvalho
Venerdì 23 ottobre 2015
Ore 14.30, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Geometria Algebrica
Ingrid Bauer (Bayreuth)
Generalized Burniat type surfaces
Generalized Burniat type surfaces are etale quotients of a hypersurface
of (2,2,2) inside a product of three elliptic curves by (Z/2Z)^3. These
surfaces are generalizations of a construction of Burniat surfaces given
by Inoue and they have invariants K^2 = 6,chi = 1. These surfaces were
completely classified and their moduli spaces were determined in a joint
paper with F. Catanese and D. Frapporti.
In the case p_g=0 Bloch's conjecture for rational equivalence classes of
zero cycles can be verified (cf. B.-Frapporti).
If a generalized Burniat type surface S is defined over the rational numbers,
then the set of rational points of S, outside a finite number of elliptic curves,
is finite. In a joint paper with M. Stoll this has been made explicit for
classical Burniat surfaces.
Venerdì 23 ottobre 2015
Ore 15.30, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Geometria Algebrica
Fabrizio Catanese (Bayreuth)
On the classification of surfaces of general type with q=p_g=1
It is well known that for minimal surfaces of general type with q = p_g=1
the invariant K^2 can take values K^2= 2,...9.
The fine classification for K^2=2,3 was achieved some years ago, and it
required the development of several tools, in joint works with Ciro
Ciliberto and Roberto Pignatelli. Existence for each value of K^2 was shown
through the work of several authors, which I shall briefly survey. I shall
then describe several recent results, obtained with Ingrid Bauer and Davide
Frapporti, and then I shall speak on work in progress with Toledo, Stover
and Keum on the geometric construction of the case K^2=9, whose existence
was shown by Cartwright and Steger using computer calculations.
Venerdì 23 ottobre 2015
Ore 16.45, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Geometria Algebrica
Xavier Roulleau (Poitiers)
An effective construction of degree 8 surfaces in P^4 with 40 nodes
Joint work with Joint work with Carlos Rito and Alessandra Sarti.
Using smoothing technics, Schoen constructed a family of surfaces S with
K^2=2, c_2=16, q=4, which have many remarkable properties.
In a previous work with C. Ciliberto and M. Mendes-Lopes, we proved that
a Schoen surface S are double cover of a degree 8 complete intersection
surface in P^4 with 40 nodes (which is the maximal number possible).
In this talk we construct in an effective way a degree 8 complete
intersection surface Z in P^4 with 40 nodes, using the geometries of
quartic K3 surfaces with 15 nodes, the Segre cubic threefold and the
Igusa quartic threefold.
A double cover S of Z branched over the 40 nodes has the same invariants
as the Schoen surface S and we prove that it is not isogeneous to a higher
quotient. We then exhibit an example of a surface Swith maximal Picard
number and a large group of symmetries.
Venerdì 23 ottobre 2015
Ore 17:00, aula I
Ortensia Mele (Formatrice Movimento di Cooperazione Educativa)
La scelta educativa della metodologia della ricerca fra neuroscienze
e pedagogia attiva
Perché ci piace cercare il nuovo e raggiungere nuove conoscenze?
Vengono presentati alcuni risultati di neuroscienziati che studiano il Sistema
della Ricerca che è tra i sistemi emozionali più attivi di cui
è dotato il cervello umano, e che è responsabile del comportamento
esplorativo e dei suoi piaceri. 'Tutti i buoni insegnanti stimolano il Sistema
della Ricerca quando rendono l'apprendimento un'esperienza avvincente piuttosto
che un mero esercizio mnemonico'.
Venerdì 23 ottobre 2015
Ore 17.45, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Geometria Algebrica
Mikhail Zaidenberg (Grenoble)
Flexibility in affine and projective geometry
The talk consists in two parts. In the first part, flexible affine varieties
are defined, different criteria of flexibility are discussed, numerous
examples and constructions of flexible varieties are presented. In the
second part, we present results on flexibility of affine cones over Fano
varieties of dimension 2, 3 and 4. For instance, del Pezzo cones demonstrate
flexibility in degree greater than 3 and rigidity in degree less than 4.
The talk is based on work of a number of persons; their names will be mentioned.
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