Notiziario Scientifico

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

Settimana dal 30 maggio al 5 giugno 2016


Lunedì 30 maggio 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
G. Scilla
Chirality transitions in frustrated ferromagnetic spin chains: a link with the gradient theory of phase transitions
We study chirality transitions in frustrated ferromagnetic spin chains, in view of a possible link with the theory of Liquid Crystals. A variational approach to the study of these systems has been recently proposed by Cicalese and Solombrino (J. Nonlinear Sci. '15), focusing close to the helimagnet/ferromagnet transition point. We reformulate this problem in the framework of surface energies in nonconvex discrete systems with NN and NNN interactions and we link it to the gradient theory of phase transitions, by showing an equivalence by Gamma-convergence with Modica-Mortola type functionals. Joint work with Valerio Vallocchia.


Lunedì 30 giugno 2016
Ore 11:00, aula Seminari (RM004), dipartimento S.B.A.I.
Seminario di Analisi Matematica
Masahiro Yamamoto (University of Tokyo)
Mathematical analysis for inverse problems: around the viscoelasticity
In mathematical physics and other fields, numerous types of inverse problems appear, where we are requested to determine and estimate physical parameters such as elasticity coefficients by available partial information of solution. My talk will start with a short introduction about what the inverse problem is, and then formulate mathematical issues such as the uniqueness and the conditional stability on the basis of concrete inverse problems. Finally I present some recent mathematical results concerning inverse problems of determining spatially varying elasticity coefficients in viscoelasticity equations.


Lunedì 30 maggio 2016
Ore 14:30, aula di Consiglio
Seminario di Analisi Matematica
Alfonso Sorrentino (Università di Roma Tor Vergata)
On the Homogenization of the Hamilton-Jacobi Equation
In this talk, we shall discuss how to extend the celebrated work by Lions, Papanicolau and Varadhan on the Homogenization of Hamilton-Jacobi equation beyond the Euclidean setting, generalising a recent result by Contreras, Iturriaga and Siconolfi.


Martedì 31 maggio 2016
Ore 14:00, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Equazioni Differenziali
Luca Biasco (Università di Roma Tre)
KAM theory for secondary tori
In general, in the phase space of nearly-integrable Hamiltonian systems may appear, near simple resonances, 'secondary' invariant tori, which are not continuation of integrable Lagrangian tori. We discuss a theory -in the case of analytic mechanical systems- apt to deal with 'most' secondary tori, under suitable generiticity conditions. This is joint work with Luigi Chierchia.


Martedì 31 maggio 2016
Ore 15:00, aula di Consiglio
Seminario di Modellistica Differenziale Numerica
Andrea Aspri (Sapienza Università di Roma)
A linear elastic model to detect magma chamber
In this seminar I will present a physical model used in volcanology to describe grounds deformations within calderas. Based on the linear elastic theory, this analytical model replaces caldera with a homogeneous, isotropic half-space and the magma chamber by a pressurized cavity of small dimensions compared to its depth. I will exhibit results on the well-posedness of this problem and then the asymptotic formula for the solution within the framework of layer potentials techniques. In the second part of the talk I will show the application of the boundary elements method to a simplified version of the elastic model, in order to discretize the direct problem and generate synthetic data for the study of the inverse problem. This is a joint work with Corrado Mascia and Elena Beretta.


Martedì 31 maggio 2016
Ore 16:00, aula L3, Università di Roma Tor Vergata
Seminario INCA-ABACO
Massimo Bernaschi (IAC-CNR)
Nuove piattaforme e paradigmi per il calcolo parallelo
Il calcolo parallelo appare come un'idea intuitiva la cui realizzazione pratica ha incontrato, tuttavia, una serie di difficoltà tali per cui è diventato solo di recente uno strumento ampiamente utilizzato dai ricercatori di varie discipline. Attraverso alcuni esempi verranno illustrate le possibilità che il calcolo parallelo offre attualmente e saranno indicate le sfide teoriche e pratiche che il suo ulteriore sviluppo offre nel breve e lungo periodo.


Mercoledì 1 giugno 2016
Ore 14:30, aula di Consiglio
Seminario di Algebra e Geometria
Sergey Fomin (UMich)
Computing without subtracting (and/or dividing)
Algebraic complexity of a rational function can be defined as the minimal number of arithmetic operations required to compute it. Can restricting the set of allowed arithmetic operations dramatically increase the complexity of a given function (assuming it is still computable in the restricted model)? In particular, what can happen if we disallow subtraction and/or division? This is joint work with D. Grigoriev and G. Koshevoy.


Mercoledì 1 giugno 2016
Ore 15:30, aula 211, Università di Roma Tre, l.go san L. Murialdo 1
Seminario di Geometria
Daniel Greb (University of Diusberg-Essen)
The Miyaoka-Yau Inequality and uniformisation of canonical models
After an introduction to the basic goals and notions of higher-dimensional birational geometry and the minimal model program, I will concentrate on the case of varieties of general type. By the seminal work of Birkar-Cascini-Hacon-McKernan (~2006) the minimal model program is known to work for these, so that every smooth projective variety of general type admits a minimal as well as a canonical model. Motivated by Riemann's Uniformisation Theorem in one complex variable, I will then describe approaches to higher-dimensional uniformisation theorems. Time permitting, at the end of my talk I will explain the proof of a recent result (with Kebekus, Peternell, and Taji) that establishes the Miyaoka-Yau Inequality (MYI) for minimal varieties of general type and characterises those varieties for which the MYI becomes an equality as quotients of the unit ball by a cocompact discrete subgroup of PSU(1,n).


Mercoledì 1 giugno 2016
Ore 16:00, aula di Consiglio
Seminario di Fisica Matematica
Antonio Moro (Northumbria University)
Quasitriviality and universality of integrable conservation laws and statistical mechanics
Conservation laws, intended as nonlinear (diffusive and/or dispersive) systems of PDEs, naturally arise in a large variety of physical and mathematical problems, from fluid dynamics to differential geometry. Quasitriviality is the property of such systems that can be reduced to a system of hydrodynamic type via a quasi-Miura transformation. The quasi-Miura transformation is a powerful tool to construct formal solutions to a PDEs given any solution to the associated hydrodynamic type equation. We discuss the quasitriviality of scalar conservation laws in relation with the classical method of transport equations with a focus on the integrable viscous conservation laws. The application of the quasi-miura transformation to the hodograph equation also provides an effective method to construct perturbed solutions in both the Hamiltonian and non-Hamiltonian case. We also provide evidence of their universal behaviour in the vicinity of the critical point of gradient catastrophe. We finally propose a statistical mechanical interpretation of fundamental objects from the theory of integrable conservation laws showing how this theory can be effectively deployed for the analysis and solution of statistical mechanical models in both finite size and thermodynamic regime.


Mercoledì 1 giugno 2016
Ore 16:00, aula F, Università di Roma Tre, l.go san L. Murialdo 1
I Tè Matematica
Benedetto Scoppola (Università di Roma Tor Vergata)
I numeri nel cervello
Sebbene la ricerca neuroscientifica sia ben lontana dal comprendere il funzionamento del cervello, test cognitivi piuttosto sofisticati e tecniche di brain imaging ci permettono di comprendere alcuni aspetti della percezione della matematica. Nel seminario si descrivono alcune di queste scoperte recenti, e si discute il loro impatto sulle tecniche di insegnamento della matematica.



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