Notiziario Scientifico

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

Settimana dal 16 al 22 novembre 2015


Lunedì 16 novembre 2015
Ore 11:00, aula B
Incontro di lavoro su Calcolo delle Variazioni e Γ-convergenza/ Working seminar on Calculus of Variations and Γ-convergence
Andrea Braides (Università di Roma Tor Vergata)
Surface energies of systems of chiral molecules


Lunedì 16 novembre 2015
Ore 14:30, aula di Consiglio
Seminario di Analisi Matematica/Presentazione Tesi di Dottorato
Roberto Feola (Sapienza Università di Roma)
Quasi-periodic solutions for fully nonlinear NLS
We consider a class of fully nonlinear, autonomous and reversible Schrödinger equations on the circle and we prove the existence and the stability of Cantor families of (small amplitude) quasi-periodic solutions. The proof is based on a combination of different ideas:
(i) we perform a 'weak' Birkhoff normal form step in order to find an approximately invariant manifold on which the dynamics is approximately integrable;
(ii) we introduce a suitable generalization of a KAM nonlinear iteration for 'tame' and 'unbounded' vector fields based on the invertibility of the linearized equation in a neighborhood of the origin;
(iii) we exploit the 'pseudo-differential structure' of the vector field and we prove the invertibility of the linearized operator, using a regularization procedure which conjugates the operator to a differential operator with constant coefficients plus a bounded remainder. This latter step is obtained through transformations generated by torus diffeomorphisms and pseudo-differential operators. Then we use a KAM-like reducibility scheme that reduces to constant coefficients the linearized operator at the solution. This gives the linear stability.


Martedì 17 novembre 2015
Ore 14:30, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Equazioni Differenziali
Fabiana Leoni (Sapienza Università di Roma)
Stime locali ed esistenza globale per disequazioni completamente non lineari
Presenteremo alcuni recenti risultati riguardanti stime a priori locali per soluzioni di viscosità di disequazioni ellittiche completamente non lineari. Verranno considerate sia equazioni non proprie, ovvero con termini di ordine zero di tipo 'reazione', che equazioni proprie, cioè con termini di ordine zero di 'assorbimento'. In quest'ultimo caso i risultati sono stati ottenuti in collaborazione con I. Capuzzo Dolcetta e A. Vitolo.


Martedì 17 novembre 2015
Ore 14:30, aula De Blasi, Università di Roma Tor Vergata
Seminario di Geometria Algebrica
Karol Palka (Warszawa)
Almost minimal log surfaces and the log-MMP with half-integral coefficients
An important tool in studying open algebraic surfaces is the logarithmic Minimal Model Program. Although in dimension two its general mechanism is well understood, in concrete problems we need an analysis which goes far beyond the general framework. For log surfaces with reduced boundaries the usage of almost minimal models (due to Miyanishi, Fujita and others), which allows to avoid singularities, turned out to be very successful. Recently we generalized this approach to boundaries with coefficient 1/2 and used it in particular in the proof of the Coolidge-Nagata conjecture (2015, coauthored with M. Koras) concerning cuspidal planar curves. We will discuss a more general form of this approach showing how to apply it to other problems concerning surfaces of log general type.


Martedì 17 novembre 2015
Ore 15:00, aula di Consiglio
Seminario di Modellistica Numerica Differenziale
I. Birindelli (Sapienza Università di Roma)
On the approximation of the principal eigenvalue for a class of nonlinear elliptic operators
We will introduce the concept of the principal eigenvalue for fully nonlinear operators not in divergence form. In particular, we shall see that the principal eigenvalue can be defined through a max-min optimization problem. This will lead to an approximation of it. We will prove the convergence of the method and we discuss its implementation. Some examples where the exact solution is explicitly known show the effectiveness of the method.


Martedì 17 novembre 2015
Ore 15:30, aula D'Antoni, Università di Roma Tor Vergata
Seminario di Geometria Algebrica
Concettina Galati (Università della Calabria)
Dimostrazione della formula di Caporaso-Harris: sezioni iperpiane delle varietà di Severi, II


Mercoledì 18 novembre 2015
Ore 14:30, aula di Consiglio
Seminario di Algebra e Geometria
Alex Lubotzky (Hebrew University of Jerusalem)
From Ramanujan graphs to Ramanujan complexes
Ramanujan graphs are optimal expanders (from spectral point of view). Explicit constructions of such graphs were given in the 80's as quotients of the Bruhat-Tits tree associated with GL(2) over alocal field F, by suitable congruence subgroups. The spectral bounds were proved using works of Hecke, Deligne and Drinfeld on the 'Ramanujan conjecture' in the theory of automorphic forms. The work of Lafforgue, extending Drinfeld from GL(2) to GL(n), opened the door for the construction of Ramanujan complexes as quotients of the Bruhat-Tits buildings. This gives finite simplical complxes which on one hand are 'random like' and at the same time have strong symmetries. Recently various applications have been found in combinatorics, coding theory and in relation to Gromov's overlapping properties. We will describe these developments and some recent applications. In particular, we will present a joint work with Tali Kaufman and David Kazhdan and another one by S. Evra and T. Kaufman in which these complexes are uses to answer a question of Gromov.


Mercoledì 18 novembre 2015
Ore 15:30, aula di Consiglio
Seminario di Algebra e Geometria
Matteo Cavaleri (Sapienza Università di Roma)
Quantification and computation of soficity
In the class of finitely generated groups we introduce equivalent definitions for sofic groups, amenable groups, word problem and a quantification of soficity, the sofic dimension growth. We present the Minsky machines in order to define computability and to construct Kharlampovich group, a finitely presented solvable group with unsolvable word problem. We prove the computability of Folner sets and the non computability of sofic approximations for Kharlampovich group. More generally we study the classes of groups with computable Folner sets, with subrecursive sofic dimension growth and their stability properties.


Mercoledì 18 novembre 2015
Ore 16.00, aula F, Università di Roma Tre, largo san L. Murialdo 1
I Tè di Matematica
Alessandro Verra (Università di Roma Tre)
Alexander Grothendieck e il suo tempo


Giovedì 19 novembre 2015
Ore 10:30, aula riunioni (primo piano), IAC-CNR via dei Taurini 19
Seminario di Matematica Applicata
Paula De Oliveira (University of Coimbra)
Mathematical models: paving the way for a personalized medicine?
The transport of drug molecules in body tissues depends on their properties but also on the physiological properties of the target tissues. A compromised elasticity, a larger stiffness, an increased porosity and a chronic inflammation are common characteristics that can be found in aging tissues. The aim of this talk is to show how these properties influence the pharmacokinetics of drugs. Mathematical models that represent the coupling between drug delivery devices and body tissues are presented. Numerical simulations show how these models can pave the way for a personalized medicine.


Giovedì 19 novembre 2015
Ore 14.00, aula 211, Università di Roma Tre, largo san L. Murialdo 1
Seminario di Geometria
Alberto Bellardini (KU, Leuven)
Log smooth reduction of tamely ramified abelian varieties
Let L be complete discrete valuation field with perfect residue field k and ring of integers O. A classical theorem of Serre and Tate says that an abelian variety A over L admits a model over O which is an abelian scheme if and only if the inertia subgroup of the absolute Galois group of L acts trivially on the first l-adic étale cohomology group of A, for some l prime number different from the characteristic of k. In this talk I want to discuss a logarithmic version of this result. Namely if the wild inertia subgroup of the absolute Galois group of L acts trivially on the first l-adic étale cohomology group of A, for some l prime number different from the characteristic of k, then A admits a projective, log smooth model over O. During the talk I will recall and give examples about some basic facts on this subject, especially about log smoothness. I am not going to assume familiarity with logarithmic geometry. This is a joint work with A. Smeets.


Giovedì 19 novembre 2015
Ore 14:15, aula di Consiglio
Seminario P(n)
Nicola Soave (University of Giessen)
On entire solutions of an elliptic system modelling phase-separation
We present several results concerning existence and qualitative properties of entire solutions to a class of elliptic systems modelling phase-separation.


Giovedì 19 novembre 2015
Ore 15.00, aula A, Università di Roma Tre, via Della Vasca Navale 84
Seminario di Fisica Teorica
Luciano Maiani (Sapienza Università di Roma)
Tetraquarks, pentaquarks and dibaryons
The discovery of two pentaquarks by LHCb has reinforced the case of 'exotic' hadrons, which have diquarks and antidiquarks as basic units. I review the cases studied until now, the so called XYZ states, the theoretical basis for this concept and the implications for the existence of further states, with baryon number equal two.


Giovedì 19 novembre 2015
Ore 15.15, aula 211, Università di Roma Tre, largo san L. Murialdo 1
Seminario di Geometria
Claudio Pedrini (Università di Genova)
Bloch's conjecture and valency of correspondences for K3 surfaces
Bloch's conjecture for a surface X over an algebraically closed field k states that every homologically trivial correspondence acts trivially on the Albanese kernel of the extension of X to a universal domain containing k. Here we prove that, for a complex K3 surface X, Bloch's conjecture is equivalent to the existence of a valence for every correspondence. We also give applications of this result to the case of a correspondence associated to an automorphism of finite order and to the existence of constant cycle curves on X. Finally we show that Franchetta's conjecture, as stated by K. O'Grady, holds true for the family of polarized K3 surfaces of genus g, if g is greater or equal to 3 and smaller or equal to 6.


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