Notiziario Scientifico
Notiziario dei seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 26 febbraio al 4 marzo 2018
Lunedì 26 febbraio 2018
Ore 14:15, aula B
seminario di Analisi Matematica
Paolo Baroni (Università di Parma)
Recent updates on double phase variational integrals
I will describe, starting from a general background, some recent updates in the
regularity theory for minimizers of non-autonomous functionals of the Calculus
of Variations, so-called double phase functionals. I will try to show in this
respect how a unified proof, simpler than all the previous ones, allowed us to
catch borderline cases and to detect new, unexpected phenomena.
Martedì 27 febbraio 2018
Ore 15:00, 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.
Martedì 27 febbraio 2018
Ore 16:00, aula L
seminario sulla storia della Facoltà
Giovanni Pietro Lombardo e Giorgia Morgese (Sapienza Università di Roma)
I Contributi del Laboratorio di Psicologia sperimentale fondato da Sante De
Sanctis (1862-1935), 'Maestro della Sapienza'
Mercoledì 28 febbraio 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
15:00 Marco Rigoli (Università di Milano) Mean curvature flow solitons
16:15 Paolo Mastrolia (Università di Milano) From Ricci solitons to f-structures:
'potential' generalization of some canonical Riemannian metrics
Giovedì 1 marzo 2018
Ore 14:30, aula di Consiglio
seminario P(n)/N(p)
Vivina Barutello (Università di Torino)
Recent Results on Index Theory in Celestial Mechanics
Index Theory can be used in Celestial Mechanics both to
study linear stability of some classes of periodic orbits and to
compute the Morse Index of a huge classes of solutions. In this talk
we will focus on some recent results, that give a necessary and
sufficient condition for the finiteness of the Morse index of
trajectories interacting with the singular set and provide an Index
Theorem to link the Morse index to a finite dimensional symplectic
invariant, the Maslov Index.
Joint work with: Xijun Hu, Riccardo Jadanza, Alessandro Portaluri,
Susanna Terracini.
Giovedì 1 marzo 2018
Ore 15:00, aula Dal Passo, dipartimento di Matematica,
Università di Roma Tor Vergata, viale della Ricerca Scientifica 1
junior colloquium
Eleonora Di Nezza (Institut des Hautes Etudes Scientifiques, Paris)
Special metrics in Kähler geometry
A basic problem in geometry is to try to classify manifolds, the main object of study
for geometers. The most well known example is the Uniformization Theorem that ensures
that every orientable compact manifold of real dimension 2 admits a constant curvature
metric. There are several ways to try and generalize the Uniformization Theorem in higher
dimension. In this concerns, an interesting option is to restrict our attention to Kähler
manifolds. The problem is then to study canonical metrics in Kähler geometry. Among
those, the notion of Kähler-Einstein metrics is very important. In this talk we are going
to introduce all these notions and we show how the study of special (=Kähler-Einstein)
metrics gives insights into the classification of Kähler manifolds.
Venerdì 2 marzo 2018
Ore 12:00, aula di Consiglio
seminari MoMa
Felix Otto
Domain and wall pattern in thin-film ferromagnets
The magnetization of a ferromagnet is known to form patterns in order to minimize the sum of
exchange and stray-field energy (even in the absence of a strong crystalline anisotropy, as in
soft materials like Permalloy). Depending on the geometry of the sample, the magnetization
features domains, in which it is nearly constant, separated by comparatively sharp transition
layers (i.e. walls).
Even if the sample comes in form of a thin film (thickness in nanometer range), the energy
landscape features many local minimizers - to the effect that the switching route is complicated
and hysteresis occurs.
Despite a small film thickness, direct numerical simulation often is not an option for realistic
lateral sample sizes and material parameters: The problem resides in the widely separated length
scales and the expensive three-dimensional stray-field computation.
For a number of specific patterns, we have adopted a different strategy: After identifying the
relevant parameter regime, we derived an appropriate (dimensionally) reduced model, which capitalizes
on the scale separation, and that is numerically tractable.
We shall present several examples, including quantitative comparison with experimental data (Kerr
microscopy). Our experimental collaborator is R. Schafer (IWF Dresden).
Venerdì 2 marzo 2018
Ore 15:00, aula D'Antoni, dipartimento di Matematica,
Università di Roma Tor Vergata, viale della Ricerca Scientifica 1
seminario di Analisi Complessa
Eleonora Di Nezza (Institut des Hautes Etudes Scientifiques, Paris)
The Calabi conjecture on compact Hermitian manifolds
We present a paper of Tosatti-Weinkove on the resolution of the hermitian version of the Calabi conjecture.
More precisely, they prove that each element in the first Bott-Chern class can be represented as the first
Chern from of a Hermitian metric. The result is obtained as corollary of uniform estimates for a complex
Monge-Ampère equation type on a compact Hermitian manifold. We are going to show such estimates
(especially the C0-estimate) in detail.
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