a cura del Dipartimento 'G. Castelnuovo'

Settimana dal 19 al 25 marzo 2018

**Lunedì 19 marzo 2018**

Ore 14:00, aula I
*Incontro Scientifico su problemi ellittici dedicato a Guido Stampacchia
nel quarantennale della scomparsa*

14:00 brevi interventi di R. Salvati Manni, V. Nesi, V. Coti Zelati e C. Sbordone

14:15 N. Fusco *Asymptotic stability for the gradient flow of nonlocal energies*

15:05 G. Mingione *Recent advances in nonlinear potential theory*

16:20 L. Orsina *The strong maximum principle for the Schrödinger equation with
Borel potentials: validity and failure*

17:10 H. Brezis *On some 1-d minimization problems involving BV*

**Martedì 20 marzo 2018**

Ore 14:30, aula Dal Passo, dipartimento di Matematica,
Università di Roma *Tor Vergata*, viale della Ricerca Scientifica 1

seminario di Equazioni Differenziali

Mikaela Iacobelli (Durham University)
*Recent results on quasineutral limit for Vlasov-Poisson via Wasserstein
stability estimates*

The Vlasov-Poisson system is a kinetic equation that models collisionless plasma. A plasma
has a characteristic scale called the Debye length, which is typically much shorter than the
scale of observation. In this case the plasma is called 'quasineutral'. This motivates
studying the limit in which the ratio between the Debye length and the observation scale
tends to zero. Under this scaling, the formal limit of the Vlasov-Poisson system is the
Kinetic Isothermal Euler system.
The Vlasov-Poisson system itself can formally be derived as the limit of a system of ODEs
describing the dynamics of a system of N interacting particles, as the number of particles
approaches infinity. The rigorous justification of this mean field limit remains a fundamental
open problem. In this talk we present the rigorous justification of the quasineutral limit for
very small but rough perturbations of analytic initial data for the Vlasov-Poisson equation in
dimensions 1, 2, and 3. Also, we discuss a recent result in which we derive the Kinetic Isothermal
Euler system from a regularised particle model. Our approach uses a combined mean field and
quasineutral limit.

**Martedì 20 marzo 2018**

Ore 15:00, aula di Consiglio

seminario di Modellistica Differenziale Numerica

M. De Santis (*Sapienza* Università di Roma)
*Active-set Algorithmic Frameworks for Sparse Optimization*

In the context of sparse optimization problems, being able to quickly identify the active set
(i.e. the subset of zero components in an optimal solution) is becoming a crucial task as it can
considerably reduce the complexity of the problem.
We describe an active set estimate that tries to quickly identify as many active variables as
possible at a given point, while guaranteeing that some approximate optimality conditions are
satisfied. A relevant feature of the estimate is that it gives a reduction of the objective function
when setting to zero all those variables estimated active. This enables to easily embed the active
set estimate into a given globally converging algorithmic framework.
Some numerical results are reported to show the effectiveness of the approach.
The presented results are related to joint works with Andrea Cristofari (Università di Padova),
Stefano Lucidi (Sapienza, Università di Roma), Francesco Rinaldi (Università di Padova).

**Martedì 20 marzo 2018**

Ore 16:00, aula di Consiglio

seminario di Modellistica Differenziale Numerica

Maya Briani (CNR-IAC, Roma)
*Runge-Kutta Discontinous Galerkin methods for shallow-water equations on a
canals network*

We shall consider the one-dimensional Saint-Venant equations for the numerical simulation of
shallow water flows on a canals network. We assume that no source term is present and we deal
with the delicate problem of defining and simulating the dynamic at the canals junction.
After revisiting the basics of Runge-Kutta (RK) discontinuous Galerkin (DG) on a single canal,
we describe the numerical coupling condition at the junction according to the two main used
approaches, which impose the equality of water height and the continuity of energy (besides
the conservation of flow) between incoming and outgoing canals. We conclude giving some numerical
tests on one-to-two and two-to-one junctions.

**Mercoledì 21 marzo 2018**

Ore 15:00, aula Seminari, RM004, Dipartimento di Scienze di Base e Applicate per Ingegneria
(SBAI), via A. Scarpa 16

Incontri di Analisi MaTÈmatica allo SBAI

Andrea Moiola (Università di Pavia)
*Scattering by fractal screens: functional analysis and computation*

The mathematical analysis and numerical simulation of acoustic and electromagnetic wave scattering
by planar screens is a classical topic. The standard technique involves reformulating the problem
as a boundary integral equation on the screen, which can be solved numerically using a boundary element
method. Theory and computation are both well-developed for the case where the screen is an open
subset of the plane with smooth (e.g. Lipschitz or smoother) boundary.
In this talk I will explore the case where the screen is an arbitrary subset of the plane; in particular,
the screen could have fractal boundary, or itself be a fractal. Such problems are of interest in the
study of fractal antennas in electrical engineering, light scattering by snowflakes/ice crystals in
atmospheric physics, and in certain diffraction problems in laser optics. The roughness of the screen
presents challenging questions concerning how boundary conditions should be enforced, and the appropriate
function space setting. But progress is possible and there is interesting behaviour to be discovered: for
example, a sound-soft screen with zero area (planar measure zero) can scatter waves provided the fractal
dimension of the set is large enough. This research has also motivated investigations into the properties
of fractional Sobolev spaces (the classical Bessel potential spaces) on non-Lipschitz domains. Accurate
computations are also challenging because of the need to adapt the mesh to the fine
structure of the fractal. As well as presenting numerical results, I will outline some outstanding open
questions. This is joint work with Simon Chandler-Wilde (Reading) and David Hewett (UCL).

**Mercoledì 21 marzo 2018**

Ore 16:15, aula Seminari, RM004, Dipartimento di Scienze di Base e Applicate per Ingegneria
(SBAI), via A. Scarpa 16

Incontri di Analisi MaTÈmatica allo SBAI

Daniele Cassani (Università dell'Insubria)
*Choquard type equations with Hardy-Littlewood-Sobolev upper- and lower-critical growth*

We are concerned with a class of nonlocal Schroedinger equations which show up in many different applied
contexts. In particular we consider the case in which the nonlinear interaction has critical features.
In the classical Sobolev sense, when we are in presence of the Hardy-Littlewood-Sobolev upper-critical
exponent, as well as new critical phenomena occur, the so-called 'bubbling at infinity', when the
nonlinearity exhibits lower-critical growth. Assuming mild conditions on the nonlinearity and by using
variational methods, we establish existence, non-existence and qualitative properties of finite energy
solutions. Some partial results in the limiting case of dimension two will be also presented.
(Joint works in collaboration with: J. Zhang; J. Van Schaftingen and J. Zhang; C. Tarsi and M. Yang).

**Mercoledì 21 marzo 2018**

Ore 16:00, aula Picone

seminario di Didattica della Matematica

José Navarro (Universidad de Cadiz)
*Cominciare bene in matematica è importante!*

Navarro, psicologo dell'età evolutiva e dell'educazione, Illustra le ricerche del suo gruppo
interdisciplinare -composto da psicologi, matematici e ingegneri, educatori- con attenzione ad alcuni
processi cognitivi in relazione all'apprendimento della matematica a partire dai 4 anni.
In particolare il gruppo di occupa e segue lo sviluppo di bambini che mostrano delle difficoltà,
compreso l'autismo. Presenta alcune App per tablet ideate appositamente e sperimentate con bambini di
4-6 anni. Illustra alcuni dei materiali ideati e ampiamente utilizzati in Spagna, Cile e Perù
nel metodo ABN (Algoritmos Basados en Numeros).

**Mercoledì 21 marzo 2018**

Ore 16:00, aula Dal Passo, dipartimento di Matematica,
Università di Roma *Tor Vergata*, viale della Ricerca Scientifica 1

seminario

Wojciech Dybalski (TUM Munich)
*Infravacuum representations and velocity superselection in non-relativistic QED*

It is well established that in QED plane-wave configurations of the electron corresponding to different
velocities induce inequivalent representations of the algebra of the electromagnetic field.
This phenomenon of velocity superselection is one of the standard features of the infraparticle
picture of the electron, which relies on mild fluctuations of the electromagnetic field at spacelike
infinity. As these fluctuations are large in the complementary infravacuum description of the electron,
it has long been conjectured that velocity superselection, and other aspects of the infraparticle problem,
can be cured in this approach. We consider two implementations of the infravacuum picture in a Pauli-Fierz
model of QED. In the first one, which relies on a decomposition of the electron into the bare electron
and a cloud of soft photons, we prove the absence of velocity superselection. In the second one, which
does not rely on such a decomposition, we show that velocity superselection persists, but can be
eliminated by suitably inverting the representations. In the language of superselection theory, we
exhibit an unusual situation, where a family of distinct sectors has one and the same conjugate sector.
(Joint work with Daniela Cadamuro).

**Mercoledì 21 marzo 2018**

Ore 16:00, aula F, Università di Roma *Tre*,
largo san Leonardo Murialdo 1

colloquium di Matematica

Alexandre Stauffer (University of Bath)
*Random growth processes: dendritic formation and competition*

During the 80's, several growth processes were introduced in the
physics literature with the goal of providing a simple and tractable
model producing the phenomenon of dendritic growth.
Such phenomenon is observed in several different contexts in nature,
including the growth of bacteria under starvation, crystal dendrite,
dielectric breakdown, and electrodeposition, and is characterized by
the formation of very ramified, fractal-like structures. Almost four
decades later, we still encounter tremendous mathematical challenges
in studying the geometric and dynamic properties of such processes,
and in understanding the driving mechanism lying behind the formation
of fractal-like structures.
In this talk, I will survey the developments in this field, giving
emphasis to recent results in the classical model of multi-particle
diffusion limited aggregation (MDLA). I will also introduce and
discuss a new growth process, which can be viewed as a model for the
growth of two species that compete for space, and which plays a key
role in our current understanding of MDLA. This is based on joint
works with Elisabetta Candellero and Vladas Sidoravicius.

**Venerdì 23 marzo 2018**

Ore 11:00, aula 311, pal. C, Università di Roma *Tre*,
largo san Leonardo Murialdo 1

seminario di Logica

Paul Ruet (IRIF, Université Paris Diderot)
*Negative local feedbacks in Boolean networks*

We shall be interested in the asymptotic dynamical properties of
Boolean networks: fixed points, attractive cycles, and more general
attractors. While the properties of Boolean networks without local
cycle or without local positive cycle are rather well understood,
recent literature raises the following two questions about networks
without local negative cycle. Do they have at least one fixed point?
Should all their attractors be fixed points? We give negative answers
to both questions: we show that and-nets without local negative cycle
may have no fixed point, and that Boolean networks without local
negative cycle may have (antipodal) attractive cycles.

**Venerdì 23 marzo 2018**

Ore 16:00, aula Picone

seminario per insegnanti (Piano Lauree Scientifiche)

Stefano Finzi-Vita e Marta Menghini (*Sapienza* Università di Roma),
Francesca Coppa e Antonio Fanelli (Liceo Plinio Seniore), Francesca
Ortenzi (Liceo Azzarita), Alexander Saltuari (Liceo Majorana)
*Non si finisce mai con la sezione aurea...*

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