Notiziario Scientifico

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

Settimana dal 10 al 16 dicembre 2018


Lunedì 10 dicembre 2018
Ore 14:15, aula di Consiglio
seminario di Analisi Matematica
L. Miguel Rodrigues (Université de Rennes 1 & Institut Universitaire de France)
Stability of traveling waves in balance laws
The derivation from spectral stability of the asymptotic stability (in the sense of Lyapunov, i.e. in large time) of traveling waves of hyperbolic systems is an important question, that is still open to a large extent. Among difficulties to overcome stand three facts
* the systems under consideration are in general quasi-linear whereas the dynamics does not exhibit strong regularization effects;
* wave profiles contain in general characteristic points where, even in dimension 1, the underlying operators lose ellipticity;
* wave profiles may be discontinuous so that the perturbed evolution problem becomes of mixed initial/boundary value type with free surfaces of discontinuity.
In the present talk, based on recent contributions with Vincent Duchêne (CNRS, Rennes), we shall see how those difficulties may be bypassed relatively easily for waves of scalar balance laws in dimension 1.


Lunedì 10 dicembre 2018
Ore 14:30, aula Dal Passo, dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica 1
seminario ART
Gwyn BELLAMY (Glasgow University)
Resolutions of symplectic quotient singularities
In this talk I will explain how one can explicitly construct all crepant resolutions of the symplectic quotient singularities associated to wreath product groups. The resolutions are all given by Nakajima quiver varieties. In order to prove that all resolutions are obtained this way, one needs to describe what happens to the geometry as one crosses the walls inside the GIT parameter space for these quiver varieties. This is based on joint work with Alistair Craw. N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006


Martedì 11 dicembre 2018
Ore 14:30, aula Dal Passo, dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica 1
seminario di Equazioni Differenziali
Sunra Mosconi (Universita' di Catania)
The Schrödinger-Poisson system with sign changing potential
The Schrödinger-Poisson system describes the motion of an electrically charged Bose-Einstein condensate subjected to potential field. We will consider the problem of existence of standing waves of arbitrary high energy. By solving the Poisson equation, this results in studying a stationary non-linear Shrodinger equation with a nonlocal sign-changing potential. Standard variational method apply when considering suitable nonlinearities, but fail for the simple yet paramount case of the Gross-Pitaevski equation. We will describe the physical model, discuss the variational formulation and related literature and propose a solution in the Gross-Pitaevski setting. This is a joint work with S. Liu, University of Xiamen


Martedì 11 dicembre 2018
Ore 15:00, aula di Consiglio
seminario di Modellistica Differenziale Numerica
Elisa Iacomini (Dottorato, SBAI SAPIENZA)
Un nuovo modello multiscala per il traffico veicolare
In questo seminario presenterò un nuovo modello per lo studio del traffico veicolare che riassume in un unico scenario il punto di vista macroscopico e microscopico, evitando qualsiasi tipo di interfaccia tra le due scale. Per l'approccio macroscopico considereremo il classico modello del primo ordine di Lighthill-Witham-Richards, mentre useremo un modello di tipo Follow-the-Leader del secondo ordine per quanto riguarda la scala microscopica. Saremo così in grado di descrivere alcune dinamiche reali, evitando implementazioni complesse e risparmiando in termini di memoria e di tempo. Lo schema numerico associato risulta essere conservativo ed in grado di descrivere gli effetti tipici del secondo ordine come le onde di stop&go. Lavoro in collaborazione con Emiliano Cristiani (IAC-CNR).


Martedì 11 dicembre 2018
Ore 16:30, aula Picone
Colloquium Guido Castelnuovo
Christian Lubich (Università di Tübingen)
Dynamics, numerical analysis and some geometry
Geometric aspects play an important role in the construction and analysis of structure-preserving numerical methods for a wide variety of ordinary and partial differential equations. Here we review the development and theory of symplectic integrators for Hamiltonian ordinary and partial differential equations, of dynamical low-rank approximation of time-dependent large matrices and tensors, and its use in numerical integrators for Hamiltonian tensor network approximations in quantum dynamics.
Tutti gli interessati sono vivamente invitati a partecipare. Informazioni sui Colloquia previsti nel prossimo futuro sono disponibili al seguente link:
https://www.mat.uniroma1.it/ColloquiumGuidoCastelnuovo


Mercoledì 12 dicembre 2018
aula 1B1, Dipartimento SBAI, Via Antonio Scarpa 16
Incontri di Analisi MaTÈmatica allo SBAI

  • Ore 15:00: Arrigo Cellina (Università degli Studi di Milano-Bicocca, Milano), On the regularity of solutions to some classes of variational problems
  • Ore 15:45: Tea Break
  • Ore 16:00: Susanna Terracini (Università di Torino), The nodal set of solutions to sublinear, discontinuous and singular equations

Mercoledì 12 dicembre 2018
Ore 16:00, aula F, primo piano, edificio Aule, Università di Roma Tre, largo san Leonardo Murialdo 1
colloquium di Matematica
Gerhard Frey (University of Duisburg-Essen)
Arithmetic Geometry: Deep Theory, Efficient Algorithms and Surprising Applications
After recalling the principles of a Diffie-Hellman key exchange scheme we shall discuss algorithms for addition in divisor class groups Pic0 (C),where C is a projective curve over a finite field Fp. Of special interest are elliptic and hyperelliptic curves, and as consequence of the results one can try to use their Picard groups for cryptographic schemes based on discrete logarithms. For this, we have to test the hardness of the computation of the discrete logarithm, and it turns out that a very efficient attack based on index-calculus eliminates all curves of genus at most 4 and non-hyperelliptic curves of genus 3. Going further and using an explicit isogeny of Jacobians of hyperelliptic curves of genus 3 we have to exclude "many" hyperellipticcurves of genus 3. The good news is that the remaining curves (including nearly all curves of genus 1 and 2) are till today "exponentially secure" against all known attacks based on conventional computer algorithms, and since one can solve the point counting task for these curves in cryptographically relevant ranges we have a rather satisfying situation of cryptography based on elliptic and hyperelliptic curves-as long as we restrict the algorithms to classical bit-operations. But the possibility of the existence of quantum computers in a not too far future forces to look for alternatives since the discrete logarithm will have only polynomial complexity (key word "Shor's algorithm"). This opens a new and very interesting area of research. Amongst other proposals the idea of using isogeny graphs of elliptic curves and the hardness to compute explicitly isogenies between elliptic curves (known to be isogenous) leads to key exchange schemes away from discrete logarithms. We shall present such schemes using ordinary elliptic curves (Couveignes-Stolbunov et.al) (rather slow) and supersingular elliptic curves over prime fields Fp (W. Castrycket. al) (very fast), which are both of subexponential security. Going to supersingular curves over Fp2 we explain the scheme of De Feo, Jao et.al which is not so fast as Castryck's scheme but has, at our present knowledge, exponential security


Mercoledì 12 dicembre 2018
Ore 16:00, aula Dal Passo, dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica 1
Yusuke Isono (RIMS Kyoto)
Intertwining theory for general von Neumann algebras and applications
We investigate Popa's intertwining condition, using Tomita-Takesaki's modular theory. In particular, we give a new characterization of Popa's condition in terms of their continuous cores. In this talk, I will explain the idea and the difficulty of proving this characterization, and also mention some applications.


Mercoledì 12 dicembre 2018
Ore 17:30, aula Dal Passo, dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica 1
Kei Hasegawa (University of Kyoto)
Bass-Serre trees for amalgamated free products of C*-algebras and applications
The Bass-Serre tree associated to an amalgamated free product of groups is a tree on which the group acts in a canonical way. This action is a powerful tool in various studies of the group itself. In this talk, I will introduce its analogy for amalgamated free products of C*-algebras, and explain how ideas coming from geometric group theory can be used in the C*-algebra setting.


Giovedì 13 dicembre 2018
Ore 14:30, aula di Consiglio
seminario P(n)/N(p)
Gagriele Mancini (Sapienza Università di Roma)
Energy quantification for Moser-Trudinger type nonlinearities in dimension two
I will discuss some recent results obtained in collaboration with L. Martinazzi and P-D. Thizy concerning semilinear elliptic problems involving Moser-Trudinger type nonlinearities. After summarizing some known facts regarding the standard Moser-Trudinger critical equation, I will describe how the classical results are affected by the presence of perturbation terms. Then, I will present the answer to a question formulated by O. Druet, proving the existence of families of nonlinearities with uniformly critical growth for which the corresponding semilinear problem admits a bubbling sequence of solutions having a nontrivial weak limit.


Giovedì 13 dicembre 2018
Ore 14:30, aula Dal Passo, dipartimento di Matematica, Università di Roma Tor Vergata, via della Ricerca Scientifica 1
seminario di Algebre di Operatori
Fulvio RICCI (SNS - Pisa)
Aspetti dell'analisi sferica su spazi omogenei commutativi a crescita polinomiale
Uno spazio omogeneo M = G/K connesso di un gruppo di Lie G, con K sottogruppo compatto, si dice commutativo - si dice anche che (G,K) è una coppia di Gelfand - se l'algebra degli operatori differenziali G-invarianti su M è commutativa. Nell'analisi di funzioni e di operatori G-invarianti su M, la trasformata sferica ha un ruolo analogo a quello svolto dalla trasformata di Fourier quando M = G = Rn. Le analogie tra trasformata sferica e trasformata di Fourier classica diventano più forti utilizzando la rappresentazione, dovuta a F. Ferrari Ruffino, dello spettro di Gelfand come sottoinsieme chiuso di uno spazio euclideo. In questo seminario presentiamo risultati recenti e problemi aperti sulla caratterizzazione delle trasformate sferiche di funzioni di Schwartz su M quando G ha crescita polinomiale. N.B.: This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006



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