Notiziario Scientifico
Notiziario dei seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 13 al 19 febbraio 2017
Lunedì 13 febbraio 2017
Ore 14:00, aula Rasetti, dipartimento di Fisica
seminario delle Meccaniche
Vieri Mastropietro, (Università Statale di Milano)
Many-body localization in a fermionic chain with quasi-random
Aubry-Andrè disorder
We consider a system of interacting electrons in a one
dimensional lattice with an incommensurate Aubry-Andre'
potential. We establish persistence of ground state localization
in presence of weak many-body interaction.The proof uses a
quantum many body extension of methods adopted for the stability
of tori of nearly integrable hamiltonian systems, and relies on
number-theoretic properties of the potential incommensurate
frequency and phase. The effects of the spin and of the coupling
of different chains will be also discussed, and comparison with
recent cold atoms experiments performed.
(Phys. Rev. Lett. 115 (18), 180401 (2016), Comm. Math. Phys. (2017))
Lunedì 13 febbraio 2017
Ore 14:30, aula di Consiglio
seminario di Analisi Matematica
Sergio Polidoro (Università di Modena e Reggio Emilia)
Teoremi di tipo Liouville per operatori di evoluzione ipoellittici
Vengono presentate formule di rappresentazione per le soluzioni positive di
equazioni alle derivate parziali lineari. Si suppone che l'operatore differenziale
verifichi la condizione di ipoellitticità di Hormander e che le soluzioni
siano invarianti rispetto ad un'opportuna famiglia di traslazioni.
Attraverso le suddette formule di rappresentazione, che vengono dimostrate per
mezzo della teoria di Choquet, si ottengono risultati di tipo Liouville per le
soluzioni positive definite su tutto lo spazio Euclideo.
I risultati presentati sono stati ottenuti in un lavoro in collaborazione
con A. Kogoj e Y. Pinchover.
Martedì 14 febbraio 2017
Ore 14:00, aula di Consiglio
seminario di Probabilità e Statistica
Lorenzo Bertini (Sapienza Università di Roma)
Grandi deviazioni rispetto al moto per curvatura media
Si consideri l'equazione di Allen-Cahn in dimensione d=2 o d=3.
Effettuando un riscalamento diffusivo, per dati iniziali opportuni, la
dinamica limite dell'interfaccia tra le due fasi stabili è descritta
dal moto per curvatura media. Verrà introdotta una perturbazione
stocastica di tale equazione e analizzata la corrispondente asintotica
di grandi deviazioni nel limite di interfacce concentrate.
Il corrispondente funzionale di tasso è analogo a quello ottenuto
analizzando la convergenza variazionale dei funzionali d'azione.
La dimostrazione della stima di grandi deviazioni utilizza strumenti
di teoria geometrica della misura.
Martedì 14 febbraio 2017
Ore 14:30, aula D'Antoni, Università di Roma Tor Vergata
seminario di Equazioni Differenziali
Luca Battaglia (Sapienza Università di Roma)
Entire solutions for Liouville systems
I will consider a system of two coupled Liouville equations on the plane
R2. The system admits so-called 'scalar' solutions, namely
such that the two components u1(x),u2(x) coincide.
These solutions actually solve a scalar Liouville equation on the plane,
hence they are very well known and they have been completely classified.
On the other hand, much less is known about non-scalar solutions.
Using bifurcation theory, I will show the existence of some branches of
(non-scalar) solutions bifurcating from a scalar solution.
This is a joint work with Francesca Gladiali (Università di Sassari) and
Massimo Grossi (Sapienza Università di Roma).
Mercoledì 15 febbraio 2017
Ore 11:00, aula piano terra, IAC-CNR, via dei Taurini 19
special Lecture at IAC
Thibault Damour (Institut des Hautes Études Scientifiques, Bures sur Yvette)
Gravitational Waves and Coalescing Black Holes
Two of the most novel predictions of Einstein's theory of General
Relativity were discovered soon after its creation one century ago:
Black Holes (Schwarzschild, January 1916) and Gravitational Waves
(Einstein, June 1916). It took more than 50 years to grasp the
physical significance of these theoretical discoveries. The recent
discovery of several gravitational wave events by the two Laser
Interferometer Gravitational-Wave Observatory (LIGO) interferometers
has brought the first direct evidence for the existence of black
holes, and has also been the first observation of gravitational waves
in the wave-zone. The talk will review the theoretical developments on
the motion and gravitational radiation of binary black holes that have
been decisive in interpreting the LIGO events as being emitted by the
coalescence of two black holes. In particular, we shall present the
Effective One-Body formalism which has been crucial in allowing one to
compute the bank of 250 000 templates that has been used to search
coalescence signals, and to measure the masses and spins of the
coalescing black holes.
Mercoledì 15 febbraio 2017
Ore 16:00, aula D'Antoni, Università di Roma Tor Vergata
seminario di Topologia Algebrica
Geoffroy Horel (Paris XIII)
Some formality results over finite fields
I will explain how methods of etale cohomology can lead to formality results
over finite fields in much the same way as Hodge theory can be used to prove
formality results over the rationals. For instance, one can prove that, in
favorable cases, the singular cochains of a smooth projective varieties over
the complex numbers are formal as a differential graded algebra. The same kind
of methods also leads to a proof of the formality of certain configuration spaces.
Mercoledì 15 febbraio 2017
Ore 16:00, aula F, Università di Roma Tre,
l.go san L. Murialdo 1
colloquium di Matematica
Patrick Dehornoy (Université Caen-Normandie)
Set theory fifty years after Cohen
We present a few results of modern Set Theory, with a special emphasis
on the Continuum Hypothesis and the possibility of solving the
question after the well known negative results of Godel and Cohen. The
developments of the past two decades arguably prove that the problem
makes sense, and very recent results seem to pave the way for a
possible solution.
Mercoledì 15 febbraio 2017
Ore 16:30, aula di Consiglio
seminario di Fisica Matematica
Fumio Hiroshima (Kyushu University, Fukuoka)
Analysis of time operators
The time operator is informally defined as a symmetric operator satisfying CCR
with a given self-adjoint operator H, i.e. [H,T]=i. However it is nontrivial to
construct T associated with H, and W. Pauli mentioned at 1933 that there was no
quantum time operators associated with H having eigenvalues or being semi-bounded.
In this talk we define 5 classes of time operators from mathematical point of
view, and show that a time operator exists for a Schroedinger operator
H=(-Δ+V) with some V. Note that H is semi-bounded and has infinitely
many eigenvalues.
Giovedì 16 febbraio 2017
Ore 14:30, aula 211, Università di Roma Tre,
l.go san L. Murialdo 1
seminario di Geometria
Grzegorz Kapustka (University of Cracow/University of Zurich)
On the Morin problem
I will discuss the problem of classification of finite complete families of
incident planes in P5. First i will present a construction of a
complete family of incident planes of maximal cardinality 20 (a joint work
with M.Donten-Bury, B.van Geemen, M.Kapustka, J. Wisniewski).
Then show that the Morin problem is equivalent to the problem of classification
of nodal (2,2) divisors in P2×P2. The methods consist of
studying projective models of special hyper-Kaehler fourfolds.
Venerdì 17 febbraio 2017
Ore 10:30, aula 1B, dipartimento SBAI
seminario di Equazioni alle Derivate Parziali
Felix Otto (MPI MIS Leipzig)
Rayleigh-Benard convection: Physically relevant a priori estimates
We are interested in Rayleigh-Benard convection, by which we understand the motion
of a liquid in a container that is heated through the bottom and cooled through the
top surface. In the Boussinesq approximation, this leads to the Navier-Stokes
equations for the (divergence-free) velocity with no-slip boundary conditions
coupled to an advection-diffusion equation for the temperature with inhomogeneous
Dirichlet boundary conditions. The coupled system contains two nondimensional
parameters: The Rayleigh Number Ra, that measures the strength of the
imposed temperature gradient, and the Prandtl number Pr, that measures the
strength of viscosity over inertia. We are interested in the regime of Ra≪1,
in which case the fluid motion is turbulent and the temperature features sharp boundary
layers. One relevant way of measuring the turbulent transport is to monitor the Nusselt
number Nu, which is the time and space-averaged upwards heat flux.
Many (expensive) experiments and (large scale) numerical simulations display several
scaling regimes for Nu in terms of Ra and Pr.
It is very surprising that rigorous PDE theory in form of a priori estimates can
contribute to the understanding of these scaling regimes: In 1999, P. Constantin
and C. Doering rigorously established the upper bound Nu≈Ra1/3
(up to logarithms) in the regime of vanishing inertia, that is, for Pr=∞,
in which case the Navier-Stokes equation is replaced by the quasi-static Stokes equation.
This upper bound is consistent with the experimental and numerical data.
We present an extension to finite Prandlt Number (i.e. replacing the quasi-stationary
Stokes by the time-dependent Navier-Stokes equation): We show that the upper bound
Nu≈Ra1/3 persists as long as Pr≪Ra1/3, which
goes beyond the small-data regime for Navier-Stokes.
The proof relies on a simple but curious estimate of the transport nonlinearity in
terms of the dissipation rate. This estimate naturally leads to the L1-norm
with a singular weight depending on the distance to the no-slip boundary. Hence we need
to develop a fairly involved maximal regularity theory for the instationary Stokes
equation with no-slip boundary condition with respect to this norm. This is joint
work with A. Choffrut and C. Nobili.
Venerdì 17 febbraio 2017
Ore 11:30, aula 311, Università di Roma Tre,
l.go san L. Murialdo 1
seminario di Logica
Patrick Dehornoy (Université Caen-Normandie)
Laver tables
Discovered (or invented?) by Richard Laver in the 1990s, the tables
that are now known as Laver tables are finite structures obeying the
self-distributivity law x(yz)=(xy)(xz). Although their construction is
totally explicit, some of their combinatorial properties are (so far)
established only using unprovable set theoretical axioms, a quite
unusual and paradoxical situation. We shall explain the construction
of Laver tables, their connection with set theory, and their potential
applications in low-dimensional topology via the recent computation of
some associated cocycles.
Venerdì 17 febbraio 2017
Ore 15:00, aula di Consiglio
discussione Tesi di Dottorato
Sahar Zabad (Sapienza Università di Roma)
PDE and Dynamical Methods to Weakly Coupled Hamilton-Jacobi Systems
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