Notiziario Scientifico

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

Settimana dal 19 al 25 febbraio 2018


Lunedì 19 febbraio 2018
Ore 09:00,
2nd school and workshop Mathematical Challenges in Quantum Mechanics


Lunedì 19 febbraio 2018
Ore 14:15, aula di Consiglio
seminario di Analisi Matematica
Rafael Ruggiero (Pontificia Universidade Catolica do Rio de Janeiro)
On the stability conjecture from Mane's viewpont for geodesic flows in manifolds without conjugate points (without closing lemma)
The stabililty conjecture for geodesic flows states that the geodesic flow of a compact Riemannian manifold is Anosov if and only if it is C1 structurally stable, namely, there exists an open C1 neighbourhood of the flow where every geodesic flow is conjugate to it. The general version of the C1 stability conjecture for diffeomorphisms was proven by Mane in the 1980's and relies in an essential way on Pugh's closing lemma and Franks Lemma. The closing lemma for geodesic flows is still a very difficult open problem, while the Franks lemma was obtained by Contreras-Paternain in the 1990's and more recently by Lazrag-Rifford-Ruggiero for Mane type perturbations of the metric (applying geometric control theory). Without the closing lemma at hand, we show the C2 stability conjecture from Mane's viewpoint for compact surfaces without conjugate points and for three dimensional, quasi-convex manifolds without conjugate points. In the study of the three dimensional case Thurston's uniformization theory plays an important role. We have some generalizations to higher dimensions to the so-called generalised rank one manifolds.


Lunedì 19 febbraio 2018
Ore 14:30, aula seminari, RM004, Dipartimento di Scienze di Base e Applicate per Ingegneria (SBAI), via A. Scarpa 16
workshop Young PDE's @ Roma
14:30 Monica Clapp
15:10 Jean Baptiste Casteras
16:30 Dora Salazar
17:10 Juan Carlos Fernandez


Martedì 20 febbraio 2018
Ore 09:00,
2nd school and workshop Mathematical Challenges in Quantum Mechanics


Martedì 20 febbraio 2018
Ore 09:00, aula seminari, RM004, Dipartimento di Scienze di Base e Applicate per Ingegneria (SBAI), via A. Scarpa 16
workshop Young PDE's @ Roma
09:00 François Hamel
09:40 Virginia Agostiniani
11:00 Shengbing Deng
11:40 Stefano Vita
14:30 Eleonora Cinti
15:10 Nicola Abatangelo
16:30 'Poster Session'
17:10 Tian Xu
17:50 Alberto Farina


Martedì 20 febbraio 2018
Ore 10:30, aula Multimediale, UniNettuno, piazza Grazioli 17
workshop New Directions for Nucelar Fusion Research Envisioned at the International Level


Martedì 20 febbraio 2018
Ore 14:30, aula Dal Passo, dipartimento di Matematica, Università di Roma Tor Vergata, viale della Ricerca Scientifica 1
seminario di Equazioni Differenziali
Paolo Albano (Università di Bologna)
On the analytic regularity for operators sums of squares of vector fields
We describe the problem of the analytic and Gevrey regularity for operators sums of squares of real-analytic vector fields satisfying the Hoermander bracket generating condition.


Martedì 20 febbraio 2018
Ore 15:00, aula di Consiglio
seminario di Modellistica Differenziale Numerica
Giulio Paolucci (Sapienza Università di Roma)
Adaptive Filtered Schemes for first order Hamilton-Jacobi equations
The accurate numerical solution of Hamilton-Jacobi equations is a challenging topic of growing importance in many fields of application but due to the lack of regularity of viscosity solutions the construction of high-order methods can be rather difficult. We will consider a class of “filtered” schemes for first order evolutive Hamilton-Jacobi equations. These schemes, already proposed in the literature, are based on a mixture of a high-order (possibly unstable) scheme and a monotone scheme, according to a filter function F and a coupling parameter epsilon. This construction allows to have a scheme which is high-order accurate where the solution is smooth and is monotone otherwise. This feature is crucial to prove that the scheme converges to the unique viscosity solutions. In this talk we will present an improvement of the classical filtered scheme, introducing an adaptive and automatic choice of the parameter epsilon at every iteration. To this end, we use a smoothness indicator in order to select the regions where we can compute the regularity threshold epsilon. Our smoothness indicator is based on some ideas developed for the construction of the WENO schemes, but other indicators with similar properties can be used. We present a convergence result and error estimates for the new scheme, the proofs are based on the properties of the scheme and on the properties of the indicators. We will illustrate also a number of numerical tests confirming that the adaptive filtered scheme is very efficient in many situations and improves previous results in the literature. Joint work with Maurizio Falcone and Silvia Tozza.


Martedì 20 febbraio 2018
Ore 16:00, aula D'Antoni, dipartimento di Matematica, Università di Roma Tor Vergata, viale della Ricerca Scientifica 1
seminario di Analisi Complessa
Xavier Buff (Université de Toulouse)
Families of rational maps and dynamics
Given integers d≥2 and 2≤k≤2d-2, the family of rational maps of degree d having k distinct critical points is a smooth quasiprojective variety. We shall present results and open questions regarding subvarieties where some of the critical points are periodic. Are those subvarieties smooth, do they intersect transverally, how many connected components do they have, how do they distribute as the period tend to infinity?


Mercoledì 21 febbraio 2018
Ore 09:00,
2nd school and workshop Mathematical Challenges in Quantum Mechanics


Mercoledì 21 febbraio 2018
Ore 09:00, aula seminari, RM004, Dipartimento di Scienze di Base e Applicate per Ingegneria (SBAI), via A. Scarpa 16
workshop Young PDE's @ Roma
09:00 Veronica Felli
09:40 Dario Mazzoleni
11:00 Weiwei Ao
11:40 Giorgio Tortone
14:30 Seunghyeok Kim
15:10 Azahara de la Torre
16:30 Daisuke Naimen
17:10 Alessandro Audrito
17:50 Jean Dolbeault


Mercoledì 21 febbraio 2018
Ore 14:00, aula di Consiglio
seminario di Algebra e Geometria
Christof Geiss (UNAM, Messico, e MPIM, Bonn)
Crystal graphs and semicanonical functions for symmetrizable Cartan matrices
This is a report on a joint project with B. Leclerc and J. Schroer. Associated to a symmetrizable Cartan matrix, a symmetrizrer and an orientation we define certain quivers with relations such that the so-called locally free modules resemble the behavior of a species resp. of its preprojective algebra associated to the same data. The set of components of maximal dimension for the E-filtered representations of our preprojective algebra have a natural structure of the crystal B(∞) associated to the Cartan matrix. In an appropriate convolution algebra of constructible functions we find elements which are generically 1 on a given component of this set, and 0 on all other components. Unfortunately, the generators of our algebra do not fulfill the Serre relations. However, we conjecture that the support of the functions which belong to the Serre ideal does not have maximal dimension.


Mercoledì 21 febbraio 2018
Ore 16:00, aula Dal Passo, dipartimento di Matematica, Università di Roma Tor Vergata, viale della Ricerca Scientifica 1
seminario
Matthias Schötz (University of Würzburg)
From non-formal, non-C* deformation quantization in arbitrary dimensions to abstract O*-algebras
Starting with any hilbertisable locally convex space V (i.e. locally convex space whose topology can be described by inner products), one can construct its usual deformations by means of exponential star products (like Moyal and Wick star product) on the commutative *algebra of polynomial functions over V, and finds that there is a unique coarsest topology on the deformed *algebras making all deformed products, all evaluating functionals and the *involution continuous. While this resulting deformed *algebra has some more nice properties, e.g. it allows to incorporate elements Q,P having canonical commutation relations [Q,P] = i and to exponentiate these elements in the completion of the algebra, its topology is far from being C*, yet not even submultiplicative. So the question arises, which of the properties that make C*-algebras attractive as candidates for observable algebras in physics carry over to our construction (or to similar ones that have been examined recently on the hyperbolic disc or for the Gutt star product). The notion of an abstract O*-algebra might provide a suitable framework to examine these problems: The idea is to focus more on the properties of the ordering on a *algebra coming from a suitable set of positive linear functionals, which e.g. allows to study properties of pure states in detail, and could eventually lead to a spectral theorem for *algebras of unbounded operators by applying the Freudenthal spectral theorem for lattice ordered vector spaces.


Giovedì 22 febbraio 2018
Ore 09:00,
2nd school and workshop Mathematical Challenges in Quantum Mechanics


Giovedì 22 febbraio 2018
Ore 09:00, aula seminari, RM004, Dipartimento di Scienze di Base e Applicate per Ingegneria (SBAI), via A. Scarpa 16
workshop Young PDE's @ Roma
09:00 Aleks Jevnikar
09:40 Marta Strani
11:00 Maurizio Garrione
11:40 Tobias Weth


Venerdì 23 febbraio 2018
Ore 09:00,
2nd school and workshop Mathematical Challenges in Quantum Mechanics


Venerdì 23 febbraio 2018
Ore 14:00, aula D'Antoni, dipartimento di Matematica, Università di Roma Tor Vergata, viale della Ricerca Scientifica 1
seminario
Domenica Fiorenza (Sapienza Università di Roma)
T-duality in rational homothopy theory
Sullivan models from rational homotopy theory can be used to describe a duality in string theory. Namely, what in string theory is known as topological T-duality between K0-cocycles in type IIA string theory and K1-cocycles in type IIB string theory, or as Hori's formula, can be recognized as a Fourier-Mukai transform between twisted cohomologies when looked through the lenses of rational homotopy theory. This is an example of topological T-duality in rational homotopy theory, which can be completely formulated in terms of morphisms of L-infinity algebras. Based on joint work with Hisham Sati and Urs Schreiber (arXiv:1712.00758).


Venerdì 23 febbraio 2018
Ore 15:30, aula D'Antoni, dipartimento di Matematica, Università di Roma Tor Vergata, viale della Ricerca Scientifica 1
seminario
Laura Geatti (Università di Roma Tor Vergata)
The adapted hyper-Kaehler structure on the tangent bundle of a Hermitian symmetric space II
The cotangent bundle of a compact Hermitian symmetric space X=G/K (a tubular neighbourhood of the zero section, in the non-compact case) carries a unique G-invariant hyper-Kaehler structure compatible with the Kaehler structure of X and the canonical complex symplectic form of T*X. The tangent bundle TX, which is isomorphic to T*X, carries a canonical complex structure J, the so called 'adapted complex structure', and admits a unique G-invariant hyper-Kaehler structure compatible with the Kaehler structure of X and the adapted complex structure J. The two hyper-Kaehler structures are related by a G-equivariant fiber preserving diffeomorphism of TX, as already noticed by Dancer and Szoeke. The fact that the domain of existence of J in TX is biholomorphic to a G-invariant domain in the complex homogeneous space GC/KC allows us to use Lie theoretical tools and moment map techniques to explicitly compute the various quantities of the 'adapetd hyper-Kaehler structure'. This is part of a joint project with Andrea Iannuzzi, and this talk concludes his presentation of February 9.


Venerdì 16 febbraio 2018
Ore 16:00, aula Picone
seminario per insegnanti (Piano Lauree Scientifiche)
Ciro Ciliberto (Università di Roma Tor Vergata)
Numeri primi e somme di due quadrati
Proporrò argomenti che riguardano l'aritmetica e che partono da concetti elementari. L'obiettivo è di proporre un piano di lavoro che arrivi alla dimostrazione di un famoso teorema di Fermat che caratterizza i numeri che sono somma di due quadrati. A tale proposito è possibile un excursus sul teorema di Pitagora, sull'equazione x2+y2=z2 e sulle sue soluzioni, nonché sull'ultimo teorema di Fermat. Nel corso della 'passeggiata' sarà necessario discutere dell'infinità dei numeri primi (e delle sue varie dimostrazioni), delle congruenze modo un primo, ecc.


Venerdì 23 febbraio 2017
Ore 18:00, Università di Roma Tre, via della Vasca Navale 84
Occhi sulla Luna
Dalle 18:00 fino a mezzanotte sarà possibile per tutti osservare la Luna ai telescopi del Dipartimento. Inoltre, durante la serata studenti e ricercatori guideranno il pubblico alla scoperta dell'astronomia, della fisica e della matematica con esperimenti, laboratori, dimostrazioni scientifiche, spettacoli, conferenze e seminari divulgativi. La partecipazione è gratuita. Il programma completo è disponibile al seguente link. Allo stesso indirizzo, a partire dal 18 febbraio, potrete trovare il modulo di prenotazione per i seminari, gli spettacoli di planetario e il laboratorio Terra-Luna per i più piccoli. Tutte le altre attività non necessitano di prenotazione.



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