Notiziario Scientifico
Notiziario dei Seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dall'11 al 17 aprile 2016
Lunedì 11 aprile 2016
Ore 11:00, aula 311, Università di Roma Tre,
l.go san L. Murialdo 1
Seminario di Probabilità
Alexander I. Bufetov (CNRS I2M, Steklov, IITP RAS, NRU HSE)
Quasi-Symmetries of Determinantal Point Processes
The classical De Finetti Theorem (1937) states that an exchangeable
collection of random variables is a mixture of Bernoulli sequences.
Markov measures with full support and, more generally, Gibbs measures,
on the space of binary sequences are easily seen to be quasi-invariant
under the natural action of the infinite symmetric group. The first
result of the talk is that determinantal point processes on Z induced by
integrable kernels are also quasi-invariant under the action of the
infinite symmetric group. A key example is the discrete sine-process of
Borodin, Okounkov and Olshanski. The Radon-Nikodym derivative is a
regularized multiplicative functional on the space of configurations.
The formula for the Radon-Nikodym derivative can be seen as the analogue
of the Gibbs property for our processes.
The discrete sine-process is very different from a Gibbs measure:
for example, the rigidity theorem of Ghosh and Peres shows that the
number of particles in a bounded interval is almost surely determined
by the configuration outseide the interval.
The quasi-invariance can then informally be understood as the
statement that there are no other invariants except the number of
particles.
The second result is a continuous counterpart of the first: namely,
it is proved that determinantal point processes with integrable
kernels on R, a class that includes processes arising in random matrix
theory such as Dyson's sine-process, or the processes with the Bessel
kernel or the Airy kernel studied by Tracy and Widom, are
quasi-invariant under the action of the group of diffeomorphisms of
the line with compact support (rigidity for the sine-process has been
established by Ghosh, for the Airy and the Bessel by the speaker).
While no analogues of these results in higher dimensions are known,
in joint work with Yanqi Qiu it is shown that for determinantal point
processes corresponding to Hilbert spaces of holomorphic functions on
the complex plane C or on the unit disk D, the quasi-invariance under
the action of the group of diffeomorphisms with compact support also
holds. Quasi-symmetry theorems have an analogue also for determinantal point
processes governed by J-Hermitian kernels, such as, for example, the
Whittaker kernel: in joint work with Yanqi Qiu it is shown that adding
a particle in one half of the phase space is equivalent to removing a
particle in the other half. This can be seen as a manifestation, in
the continuous case, of particle-hole duality. This project has received
funding from the European Research Council (ERC) under the European Union's
Horizon 2020 research and innovation programme under grant agreement
No 647133 (ICHAOS).
Lunedì 11 aprile 2016
Ore 14:30, aula di Consiglio
Seminario di Analisi Matematica
un pomeriggio per festeggiare Filomena Pacella
14.30 Henri Berestycki (EHESS)
15.20 Susanna Terracini (Università di Torino)
16.10 Rinfresco
Martedì 12 aprile 2016
Ore 14:00, aula B
Seminario
Giovanni Cerulli Irelli (Sapienza Università di Roma)
Homology of smooth quiver Grassmannians of Dynkin type of
minimal dimension
Martedì 12 aprile 2016
Ore 14:00, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Equazioni Differenziali
Fabio Punzo (Università della Calabria)
Nonexistence of positive solutions for elliptic and parabolic equations
with a potential on Riemannian manifolds
In this talk I will present some results concerning nonexistence of
nonnegative, nontrivial weak solutions for a class of quasilinear elliptic
and parabolic differential inequalities with a potential on complete,
noncompact Riemannian manifolds. In particular, we investigate the
interplay between the geometry of the underlying manifold, the (power)
nonlinearity and the behavior of the potential at infinity in obtaining
nonexistence of nonnegative solutions. Such results have been recently
obtained in collaboration with P. Mastrolia (Università di Milano) and
D. Monticelli (Politecnico di Milano).
Martedì 12 aprile 2016
Ore 14:30, aula D'Antoni, Università di Roma Tor Vergata
Seminario di Geometria Algebrica
Filippo Viviani (Università di Roma Tre)
Introduzione agli invarianti di Gromov-Witten II
Martedì 12 aprile 2016
Ore 14:30, aula 311, Università di Roma Tre,
l.go san L. Murialdo 1
Seminario di Fisica Matematica
Spyros Sotiriadis (Università di Roma Tre)
Quench dynamics and memory preservation in quantum integrable systems
One of the foundations of statistical physics is that only minimal
information is required for the description of macroscopic systems.
Research in quantum one-dimensional integrable systems
out-of-equilibrium has recently revealed relaxation towards a
non-thermal statistical ensemble that violates this principle due to
the presence of an infinite number of local integrals of motion. The
information content of this ensemble remains however a riddle. By
studying the dynamics after suddenly switching-off the interactions in
an isolated quantum system (a so-called quantum quench), we will show
that the time evolution under a massive Gaussian field theory erases
all memory of non-Gaussian correlations that are present in the
initial state, keeping information only about the initial two-point
correlation function. On the other hand, in the massless case in one
spatial dimension we will show that an enormous amount of information
about the initial state survives even at infinitely large times, in
contrast to earlier expectations. We provide an intuitive explanation
of the above results based on the cluster decomposition principle and
the hydrodynamic character of the evolution. Lastly we will discuss
applications to cold atom experiments and generalisations to spin
chains.
Martedì 12 aprile 2016
Ore 15:00, aula di Consiglio
Seminario di Modellistica Differenziale Numerica
Chiara Sorgentone (KTH Royal Institute of Technology, Sweden)
A high order discretization method based on integral equations
for simulating 3D deformable drops
We consider picoliter sized water droplets immersed in a fluid with
different viscosity. At these small scales, inertial effects are
negligible, and the dynamics are governed by the Stokes equations.
With the large surface to volume ratio of these drops, the dynamics
at the interface become extremely important and it is very natural
to consider integral equations for this Stokes flow problem.
The integral equations are defined on the interfaces only, require
no meshing of the volume, and naturally incorporate the interfacial
conditions. A high order discretization based on integral equations
can be made using an accurate surface representation and quadrature
method with special attention in dealing with singularities.
We consider a representation for each drop surface in terms of a
spherical harmonics expansion, the surface counterpart to a Fourier
series for a closed curve. We focus on strategies for updating these
representations dynamically with particular attention on accuracy and
efficiency. A special quadrature method for dealing with multiple
drops and close interactions is considered. Moreover, high distortions
of the surface point distribution may arise, especially for long time
simulations; for this reason, an adaptive reparametrization procedure
has been implemented. The next step in the project is to add an
insoluble surfactant and study the effect on drop deformation.
Martedì 12 aprile 2016
Ore 15:00, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Equazioni Differenziali
Philippe Souplet (Université Paris 13)
Morrey spaces and classification of global solutions for a
supercritical semilinear heat equation
We prove the boundedness of global classical solutions for the semilinear
heat equation ut-Δu=|u|p-1u in the
whole space Rn, with n≥3 and
supercritical power p>(n+2)/(n-2).
This is proved without any radial symmetry or sign assumptions,
unlike in all the previously known results, and under decay assumptions
on the initial data that are essentially optimal in view of the known
counter-examples. Moreover, we show that any global classical solution
has to decay in time faster than t-1/(p-1), which
is also optimal and in contrast with the subcritical case.
The proof relies on nontrivial modifications of techniques developed b
y Chou-Du-Zheng (Calc. Var. PDE 2007) and by Blatt-Struwe (IMRN 2015)
for the case of convex bounded domains. It is based on weighted energy
estimates of Giga-Kohn type, combined with an analysis of the equation
in a suitable Morrey space. We in particular simplify the approach of
Blatt-Struwe by establishing and using a result on global existence
and decay for small initial data in critical elliptic Morrey spaces,
rather than ε-regularity in parabolic Morrey spaces.
Our results are actually valid for any convex, bounded or unbounded,
smooth domain. As a consequence we also prove that set of initial
data producing global solutions is open in the corresponding Morrey
topology, and we show that the so-called 'borderline' weak solutions
blow up in finite time and then become classical again and decay as
t tends to +∞.
Martedì 12 aprile 2016
Ore 16:00, aula 17, Università di Roma Tor Vergata
Seminario su CUDA
Marco Sansottera (Università di Milano)
Programmazione su schede grafiche (GPU) in CUDA
GPGPU, noto anche come GPU Computing è l'acronimo di 'general
purpose computing on graphics processing units'.
L'obiettivo del GPGPU è quello di sfruttare i processori
delle schede grafiche (GPUs) per scopi differenti da quelli tradizionali,
e.g., rendering di immagini in 3D.
Le GPU sono dei dispositivi hardware multi-core ad elevate
prestazioni in termini di capacità di calcolo parallelo e
trasmissione dati, impiegate come acceleratori per elaborazioni
estremamente esigenti per le quali le tradizionali architetture
CPU non hanno sufficienti capacità di elaborazione.
CUDA è l'architettura di elaborazione in parallelo di NVIDIA che
permette di sfruttare la potenza di calcolo delle GPU NVIDIA.
Quasi tutte le principali applicazioni video sono accelerate
mediante CUDA e l'architettura CUDA è stata accolta con
entusiasmo anche nel settore della ricerca scientifica, e.g.,
CUDA è stato impiegato per l'accelerazione di AMBER, un programma
di simulazione di dinamica molecolare usato da istituti
accademici e aziende farmaceutiche di tutto il mondo.
Questa presentazione è rivolta a studenti che hanno acquisito
una discreta conoscenza della programmazione, in particolare del
linguaggio C. L'obiettivo è quello di mettere a disposizione
degli studenti gli strumenti di base e l'assistenza necessaria
per poter sfruttare la potenza di calcolo delle GPU utilizzando
il CUDA. Durante la presentazione verranno presentate alcune
applicazioni riguardanti il problema degli N-corpi ed il modello
FPU.
Mercoledì 13 aprile 2016
Ore 14:30, aula di Consiglio
Seminario di Algebra e Geometria
Julia Sauter (Bielefeld)
On quiver Grassmannians and orbit closures for
representation-finite algebras
We show that Auslander algebras have a unique tilting and cotilting
module which is generated and cogenerated by a projective-injective;
its endomorphism ring is called the projective quotient algebra.
For any representation-finite algebra, we use the projective quotient
algebra to construct desingularizations of quiver Grassmannians,
orbit closures in representation varieties, and their
desingularizations. This generalizes results of Cerulli Irelli,
Feigin and Reineke. (This is a joint work with Bill Crawley-Boevey,
who will attend the talk.)
Mercoledì 13 aprile 2016
Ore 14:30, aula Zorzi (ex-Mattatoio), Università di Roma
Tre, l.go G.B. Marzi 10
Seminario Formulas
Renato Spigler (Università di Roma Tre)
La matematica di Kuramoto per descrivere fenomeni di sincronizzazione
I cosiddetti 'modelli di Kuramoto' e altri simili modelli, rappresentano una
modo paradigmatico per descrivere una serie di fenomeni di sincronizzazione.
Questi sono 'stati' in cui sistemi incoerenti possono andare, come spesso accade
nelle transizioni di fase, e riguardano un notevole varietà di casi, che
vanno dalla Fisica alle Neuroscienze, dalla Biologia all'Ingegneria ed anche
alle Scienze Sociali. Essi spiegano, almeno qualitativamente, una grande varietà
di processi complessi. In questo seminario, passiamo in rassegna tali modelli e la
matematica sottostante, mostrando alcune delle loro peculiarità.
Giovedì 14 aprile 2016
Ore 11:15, aula riunioni (primo piano), IAC-CNR, via dei Taurini 19
Seminario di Matematica Applicata
Davide Poggiali (Università di Padova)
Th3 nub3rs 0f a br41n. Mathematics behind popular algorithms
in today's Neuromaging
In Neuroscience study, imaging systems as Magnetic Resonance Imaging (MRI)
and Positron Emission Tomography (PET) has assumed a crucial role in the
last years. To extract quantitative information from MRI and PET images,
many mathematical algorithms has been gathered into widely used software
suites as Freesurfer, SPM, FLS or the most recent ANTs.
A good knowledge about such algorithm is useful in order to correctly
choose optional parameters and to avoid misuse.
In this talk some important algorithm of image will be presented,
explained in detail and showed in action with some examples. In
particular we will focus on MRI segmentation, registration, cortical
thickness evaluation, and PET compartment models.
Giovedì 14 aprile 2016
Ore 14:15, aula di Consiglio
Seminario P(n)
Aleks Jevnikar (Università di Roma Tor Vergata)
The Toda system on compact surfaces
We consider the Toda system, namely a coupled system of Liouville
equations defined on a compact surface, which is motivated by the
study of models in non-abelian Chern-Simons theory. We will
present the known results and some more recent existence result based
on variational methods and Moser-Trudinger inequalities.
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