Notiziario Scientifico
Notiziario dei Seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 14 al 20 marzo 2016
Lunedì 14 marzo 2016
Ore 10:00, aula B
Incontro di lavoro su Calcolo delle Variazioni e Γ-convergenza/
Working seminar on Calculus of Variations and Γ-convergence
Maria Stella Gelli (Università di Pisa)
Lower-semicontinuity and relaxation results for energies in capillarity problems
The free energy in capillarity problems usually consists of a
surface term accounting for the liquid-gas interface and a 'wetting'
term accounting for the interaction at the walls of the container of the
liquid-solid phases. This last term plays a relevant role in the study of
the equilibrium surfaces and the associated Young's law. In order to
establish existence results when the container is only Lipschitz
regular I will provide structure conditions on the surface density and on
the adhesion coefficient that ensure the lower semicontinuity of the
(total) free energy with respect to the convergence in measure of sets.
I will discuss the optimality of the bounds appearing in the l.s.c. theorem
through suitable counterexamples and taking into account the 'regularity'
of the surface energy density. When the structure conditions above are
violated I will give a description of the relaxed functional.
Eventually, I will apply the lower semicontinuity result to detect the capillarity
equilibrium surfaces in case: (a) the adhesion coefficient is discontinuous;
(b) the external normal to the boundary of the container is discontinuous,
discussing in both cases the validity of Young's law.
Lunedì 14 marzo 2016
Ore 14:30, aula di Consiglio
Seminario di Analisi Matematica
Tobias Weth (University of Frankfurt)
A nonvanishing result for the Helmholtz resolvent and applications
I will discuss a nonvanishing result for the Helmholtz resolvent operator in the
spirit of Lions' first Lemma on concentration compactness. The result will be
applied to prove the existence of standing wave solutions to nonlinear Helmholtz
equations with power type nonlinearities. To detect these solutions, we need to
set up a dual variational framework. Classical direct methods in critical point
theory do not apply to this problem due to the lack of Fredholm properties.
This is joint work with Gilles Evequoz.
Martedì 15 marzo 2016
Ore 10:00, aula Attavanti, Argiletum, Università di Roma Tre,
via Madonna dei Monti 40
Minicorso
Vieri Benci (Università di Pisa)
Generalized Functions and Mathematical Modeling I
Exposition of the main ideas through meaningful examples. A generalization of
the notion of limit: the Λ-limit. Non-standard analysis.
Martedì 15 marzo 2016
Ore 14:30, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Equazioni Differenziali
Isabeau Birindelli (Sapienza Università di Roma)
Symmetry and spectral properties for viscosity solutions of fully
nonlinear equations
We will talk about the property inherited by a viscosity solution of a rotationally
invariant equation of the form F(x,D2u)+f(x,u)=0, in relation with
the spectral property of the 'improperly called' linearized operator at u.
We will show applications of our symmetry results to obtain bounds on the spectrum
and to deduce properties of possible nodal eigenfunctions for the operator.
Martedì 15 marzo 2016
Ore 15:00, aula di Consiglio
Seminario di Modellistica Differenziale Numerica
Andrea Di Mascio (IAC-CNR)
Simulazione di flussi con superficie libera mediante metodi
Lagrangiani/Euleriani accoppiati
Il seminario presenterà la ricerca in corso circa la simulazione numerica
di flussi viscosi con superficie libera, in presenza di elevata deformazione e
frammentazione del fronte d'onda. Dopo una breve descrizione del problema e un
richiamo delle metodologie attualmente in uso per la sua simulazione numerica,
verrà discussa la maniera in cui è possibile sfruttare al meglio,
tramite decomposizione del dominio, le caratteristiche di schemi formulati su
reticoli Euleriani (di tipo Volumi Finiti) e di schemi formulati in ambito
Lagrangiano (quali 'Smoothed Particle Hydrodynamics'). Verrà quindi illustrata
una maniera con cui è possibile realizzare l'accoppiamento spaziale e temporale
degli schemi discreti, in modo da ottenere soluzioni regolari alle interfacce.
L'accuratezza delle soluzioni e l'efficienza degli algoritmi verrà infine discussa.
Martedì 15 marzo 2016
Ore 15:00
Diretta Streaming del Diderot
Mathematical forum 2016
Le conferenze verrano proiettate nell'aula seminari dell'IAC (aula 116, primo piano,
IAC-CNR, via dei Taurini 19) e sarà possibile porre domande via twitter.
15:00 Marie Doumic Jauffret (INRIA Paris)
Modelling protein aggregation: results and open questions
16:15 Miguel Angel Herrero (Universidad Complutense de Madrid)
Mathematical models in biomedicine: looking for simplicity in a complex world
17:30 Alfio Quarteroni (EPFL)
Modelling the heart and the circulatory system: a challenge for
mathematicians, an opportunity for clinicians
Martedì 15 marzo 2016
Ore 16:00, aula I
Seminario per insegnanti (Piano Lauree Scientifiche)
Anna Baccaglini-Frank (Sapienza Università di Roma)
Attività CLIL: un'esperienza di matematica in inglese II
Martedì 16 marzo 2016
Ore 16:00, aula Dal Passo, Università di Roma Tor Vergata
Seminario
Yusheng Feng (University of Texas)
Mathematical Modeling and Multi-Scale Computer Simulation of Tissue Growth for
Cancer Prognosis and Treatment Planning
Cancer is the second leading cause of death in the United States and in the world.
With the advancement of computational mathematics, big data science and unprecedented
computing power, it becomes possible to investigate the complex tissue growth phenomenon
of tumors for cancer prognosis using mathematical modeling and computer simulation.
The growth of biological tissue is a complex process because it involves various
biophysically- and biochemically and biophysically-induced events at different
spatial and temporal scales. Multi-scale modeling techniques allow us to incorporate
important features at various levels to examine the tissue growth mechanism and
determine the major factors affecting the growth process. In this talk, I will discuss
a multi-scale modeling framework across tissue level, cellular and sub-cellular levels,
along with the solution strategies, and followed by some preliminary results.
Finally, I will discuss future challenges in cancer modeling.
Mercoledì 16 marzo 2016
Ore 10:00, aula Attavanti, Argiletum, Università di Roma Tre,
via Madonna dei Monti 40
Minicorso
Vieri Benci (Università di Pisa)
Generalized Functions and Mathematical Modeling II
Generalized solutions in PDEs. Ultrafunctions. Distributions.
Mercoledì 16 marzo 2016
Ore 14:30, aula di Consiglio
Seminario di Algebra e Geometria
Alessandra Iozzi (ETH)
Irreducible lattices and bounded cohomology
We show some of the similarities and some of the differences between
irreducible lattices in product of semisimple Lie groups and their
siblings in product of locally compact groups. In the case of
product of trees, we give a concrete example with interesting
properties, among which some in terms of bounded cohomology
and quasimorphisms.
Mercoledì 16 marzo 2016
Ore 14:30, aula 204, Università LUISS, viale Romania 32
Decision Sciences Community Seminars
Peter Tankov (Université Paris 'Diderot' (Paris 7))
Asymptotic Lower Bounds for Optimal Tracking: a Linear Programming Approach
We consider the problem of tracking a target whose dynamics is modeled by a
continuous Ito semi-martingale. The aim is to minimize both deviation from the
target and tracking efforts. We establish the existence of asymptotic lower bounds
for this problem, depending on the cost structure. These lower bounds can be related
to the time-average control of Brownian motion, which is characterized as a deterministic
linear programming problem. A comprehensive list of examples with explicit expressions
for the lower bounds is provided. Joint work with Jiatu Cai and Mathieu Resenbaum,
paper available here.
Mercoledì 16 marzo 2016
Ore 16:30, aula III
Seminario di Dipartimento
Lucio Russo (Università di Roma Tor Vergata)
Il metodo di Euclide e la fortuna degli 'Elementi' dall'antichità
ad oggi
Dopo avere richiamato gli elementi essenziali del metodo euclideo, si ripercorre
rapidamente la storia della considerazione in cui gli Elementi sono stati tenuti
nei ventitre secoli successivi a Euclide e le ragioni che possono consigliare oggi
di riprenderne la lettura.
Giovedì 17 marzo 2016
Ore 14:15, aula di Consiglio
Seminario P(n)
Habib Fourti (University of Sfax, Tunisia)
Harmonic functions with nonlinear Neumann boundary condition and their
Morse indices
We will study qualitative properties of solutions of a nonlinear Neumann elliptic
equation posed in a bounded open smooth domain of dimension greater or equal than two
and where the non-linearity satisfies super-linear and subcritical growth conditions
and some other assumptions.
We will prove that proving that a solution is bounded is equivalent to show that its
Morse index is bound. This result is similar to that of A. Bahri, P.L. Lions ['Solutions
of superlinear elliptic equations and their Morse indices', Comm. Pure. App. Math. 45
(1992), 1205-1215].
To prove the a priori estimate, we used a blow-up argument which leads to deal with a
Liouville type problem posed in the half space. We prove that this limit problem does
not possess nontrivial bounded solution with finite Morse index provided that
1<p<N/(N-2) if N is greater or equal than 3 and p>1 if
N is equal to 2. In this talk, I will focus mainly on the proof of this Liouville
type theorem: I will prove some integrable conditions on its solution, then I will use the
Pohozaev identity to prove the nonexistence result. This is a joint work with Mohamed
Ben Ayed and Abdelbaki Selmi.
Venerdì 18 marzo 2016
Ore 11:30, sala Ingegneria Geotecnica, Dipartimento di Ingegneria Strutturale
e Geotecnica
Seminario
Giuseppe Saccomandi (Università di Perugia)
Inseguendo una curva: come descrivere i dati di Treloar in estensione semplice
per una gomma
Venerdì 18 marzo 2016
Ore 12:00, aula di Consiglio
Seminari MoMa
Piero Manfredi
Herpes Zoster (Exogenous boosting, progressive immunity and the dilemma of
mass varicella immunization)
Herpes zoster (HZ) is a painful disease caused by the reactivation of the varicella
zoster virus (VZV) as cell mediated immunity (CMI) goes down (e.g. with ageing).
Hope-Simpson formulated (1965) the 'exogenous boosting' hypothesis (EBH), according
to which further infective exposures to VZV may boost CMI, resulting in a protective
effect against HZ. Inclusion of the exogenous boosting hypothesis in VZV transmission
models predicts a large transient wave in natural HZ incidence following mass varicella
immunization. The fear of this HZ 'boom' is a main responsible of the current stall
of varicella vaccination in Europe. In this talk, I summarize recent results from a
model incorporating a further noteworthy Hope-Simpson's hypothesis, stating that each
VZV re-exposure increases CMI protection against HZ to levels higher than those
conferred by previous ones. The 'progressive immunity' model fits well available
European HZ data, suggesting that the mechanism may be critical in shaping HZ patterns.
The model suggests counter-intuitive implications of varicella immunization in relation
to vaccine-related HZ and the epidemiology of HZ after varicella elimination.
I conclude by discussing the challenges for future VZV research.
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