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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