Notiziario Scientifico

Notiziario dei Seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma

Settimana dal 11 al 17 luglio 2016


Lunedì 11 luglio 2016
Ore 17:15, aula di Consiglio
Seminario di Probabilità
Frederic Patras (CNRS Laboratoire J.A. Dieudonné)
Free cumulants and half-shuffles
The theory of free probabilities has various origins: among others the theory of solutions of random operator-valued differential equations and the one of random matrices and their asymptotic properties. A notion of (free) cumulant has been introduced in this context which (for plenty of reasons) happens to be the 'good' generalization of classical cumulants. Roland Speicher has introduced and studied these cumulants form a combinatorial point of view, using the poset of non-crossing partitions. The talk will survey these results and explain a new approach to these questions (j.w. with K. Ebrahimi-Fard).


Martedì 12 luglio 2016
Ore 14:30, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Analisi ed Equazioni Differenziali
Matteo Bonforte (Universidad Autonoma de Madrid)
Nonlinear and Nonlocal Degenerate Diffusions on Bounded Domains
We investigate quantitative properties of nonnegative solutions u to the nonlinear fractional diffusion equation (with diffusion operator L) posed in a bounded domain with appropriate homogeneous Dirichlet boundary conditions. As L we can use a quite general class of linear operators that includes the three most common versions of the fractional Laplacian s, with s∈(0,1), in a bounded domain with zero Dirichlet boundary conditions, but it also includes many other examples, since our theory only needs some basic properties that are typical of 'linear heat semigroups'. The nonlinearity is assumed to be increasing and is allowed to be degenerate, the prototype being |u|m-1u, with m greater than 1. We will present some recent results about existence, uniqueness and a priori estimates for a quite large class of very weak solutions, that we call weak dual solutions. We then show sharper lower and upper estimates up to the boundary, which fairly combine into various forms of Harnack inequalities. The standard Laplacian case s=1 is included and the linear case m=1 can be recovered in the limit in most of the results. In these cases global Harnack estimates are the key tool to understand the sharp asymptotic behaviour of the solutions. We finally show that solutions are classical, and even C in space in the interior of the domain, when the operator L is the (restricted) fractional Laplacian. The above results are contained on a series of recent papers with J. L. Vazquez, and also with A. Figalli, Y. Sire and X. Ros-Oton.


Giovedì 14 luglio 2016
Ore 11:00, aula di Fisica Tecnica, DIAEE, via Eudossiana 18
Seminario
Valeria La Saponara (University of California, Davis)
Assessing the structural health of carbon/epoxy I-beams under bending: application of electrical resistance and ultrasonic sensors
Carbon fiber-reinforced polymer (CFRP) composite materials are used in a variety of structures in aerospace, wind energy, naval, civil and transportation applications. In this study, two structural health monitoring methods are investigated to determine their ability to track strain and damage of CFRP I-beams under bending. Method A consists of tracking electrical resistance changes from the conductive carbon fibers themselves. Method B is based on the analysis of ultrasonic waveforms launched by surface-mounted off-the-shelf piezoelectric transducers. The waveforms are processed through contours of the signals' Gabor wavelet transforms, a technique that has been successfully applied to track global damage in monolithic fiberglass/epoxy composites under uniaxial tension, and to track deflection in polymeric sandwich composites under creep bending at elevated temperatures. The applicability of both methods has yet to be explored for specimens scaled up to a structural CFRP I-beam. In this study, 1.2 m long I-beams are designed and built out of carbon/epoxy with varying fiber orientations in the web and flanges. First, sections of the I-beam are tested under four-point bending, to characterize the two sensor's sensitivity at the coupon scale, applied to both the tensile and compressive sides of the coupons. Then, the full-scale beams are loaded on a custom-made test stand, where the root of the beam is clamped and a load is applied at the tip, utilizing a compressive based load cell to measure the force, and a string potentiometer for the measurement of the tip deflection. Both the tensile and compressive sides of the beams are instrumented and monitored simultaneously. The sensitivity and limitations of both methods are assessed.


Giovedì 14 luglio 2016
Ore 14:30, aula 211, Università di Roma Tre, l.go san L. Murialdo 1
Seminario di Geometria
Antonella Grassi (University of Pennsylvania)
Noether-Lefschetz torico


Giovedì 14 luglio 2016
Ore 14:30, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Analisi ed Equazioni Differenziali
Mat Langford (Freie Universität)
Slowly forming singularities of the mean curvature flow
We will consider translating solutions of the mean curvature flow (or translators for short); that is, solutions of the mean curvature flow which evolve purely by translation. Strictly convex translators are of particular interest, as they arise as 'blow-up limits' of singularities of mean convex mean curvature flow. It was a longstanding conjecture that strictly convex translators should be rotationally symmetric. This was famously proved, by X.J. Wang, to be true in two space dimensions, but false in all higher dimensions; however, the question remained open for translators which arise as blow-ups of singularities. It was recently proved by Haslhofer that two-convex, non-collapsing translating solutions are necessarily rotationally symmetric. It then follows from a result of Andrews that any translator which arises as a blow-up limit of a two-convex embedded mean curvature flow is necessarily rotationally symmetric. We will show how to remove the non-collapsing assumption in spatial dimensions n≥3 by instead making use of estimates of Huisken and Sinestrari. As a consequence, we deduce that any translator which arises as a blow-up limit of a two-convex immersed mean curvature flow is necessarily rotationally symmetric.



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