Weekly Bulletin (it)

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

Settimana dal 25 giugno al 1 luglio 2018

Lunedì 25 giugno 2018
Ore 10:30-15:30, aula di Consiglio
Master in Calcolo Scientifico
Presentazione dei rapporti di tirocinio degli studenti del Master 2016/17

Lunedì 25 giugno 2018
Ore 17:30, aula 1B1, Dipartimento di Scienze di Base e Applicate per Ingegneria (SBAI), via A. Scarpa 16
seminario di Algebre di Operatori
Daniel Goncalves
Infinite alphabet edge shift spaces: an approach via (ultra) graphs and C*-algebras
We start the talk with an overview of (one-sided) shift spaces over infinite alphabets. Then we explain the notion of ultragraphs, wich generalize directed graphs, and use this combinatorial objects to define a notion of (one-sided) edge shift spaces (which, in the finite case, coincides with the edge shift space of a graph). We motivate why these (ultra) graph shift spaces are the natural shifts to be considered in connection with C*-algebra theory. To end we describe Li-Yorke chaos in ultragraph shift spaces and show that these shifts behave similarly to edge-shifts over finite graphs.

Mercoledì 27 giugno 2018
Ore 14:00, aula di Consiglio
seminario di Algebra e Geometria
Sebastien Boucksom (CNRS - CMLS)
Valuations, filtrations and K-stability
The notion of K-stability of a polarized projective variety, initially introduced in the context of Kähler geometry as the algebro-geometric counterpart to the existence of special Kähler metrics of constant curvature, has recently proved to be a key notion in moduli problems. Checking K-stability of a given variety is however a difficult problem, and I will present in this talk an approach to K-stability based on valuations and non-Archimedean geometry, introduced by Jonsson and myself and further developped by Fujita, Li, Odaka.

Mercoledì 27 giugno 2018
Ore 16:00, aula F, Università di Roma Tre, largo san Leonardo Murialdo 1
colloquium di Matematica
Antonino Sgalambro (University of Sheffield, CNR)
On Carriers collaboration in Hub Location
Hub location is nowadays one of the most studied areas within locational analysis, because of its wide range of practical applications, and due to the high economic impact of the decisions encompassed in these problems. In this work we consider hub location problems based on different classesof collaboration agreements among multiple carriers. Carriers collaboration models are compared by analyzing in each case the potential savings obtained with respect to a purely competitive model. Mixed integer programming formulations are proposed and computationally tested. Numerical results from such a computationalexperience are presented and analyzed, gathering useful managerial insights.

Mercoledì 27 giugno 2018
Ore 16:15, aula Picone
seminari di Fisica Matematica
16:15 Daniele Dimonte (SISSA, Trieste)
Effective Dynamics of Bose-Einstein Condensates in the Thomas-Fermi Limit
We discuss the time-dependent Gross-Pitaevskii (GP) approximation for interacting bosons in the Thomas-Fermi (TF) regime, i.e., for a mean-field interaction potential with shrinking support and whose scattering length diverges in the large N limit (but the gas remains dilute). Under these assumptions, the many-body Schrödinger dynamics is expected to be approximated by a one-particle nonlinear Schrodinger equation: the reliability of this approximation is the problem we plan to investigate. While the mean-field or GP limits have already been studied in detail, and the approximation proven to be correct on suitable time scales, the TF limit has never been studied, in spite of its large relevance in experimental physics. We show that the question of the dynamic approximation is more subtle in the TF regime, in particular at large time scales. The results are proven by exploiting the method developed by P. Pickl. Joint work in progress with M. Correggi, D. Mitrouskas and P. Pickl.

17:00 Alessandro Olgiati (SISSA, Trieste)
Effective description of mixtures of condensates
I will present rigorous results on the effective properties of many-body systems consisting of multiple bosonic species. This will be based on joint works with A. Michelangeli and P.T. Nam. Concerning stationary properties, we were able to prove that, both in the mean field and Gross-Pitaevskii regime, the leading order of the ground state energy is captured by the minimum of a suitable effective functional. Moreover, in the ground state, all species of the mixture exhibit condensation. For mixtures in the mean field regime, we are also able to justify Bogoliubov theory, hence computing the next-to-leading correction to the ground state energy, and proving a norm approximation for the ground state. The above properties justify crucial assumptions for the theorems on the dynamical evolution that I will present. These are results of persistence of condensation for mixtures, which I will state and discuss both in the mean-field and Gross-Pitaevskii regime.

17:45 Raffaele Scandone (SISSA, Trieste)
On Schrödinger Operators with Point Interactions
A central topic in mathematical physics is the investigation of quantum systems subject to very short range potentials, virtually supported on a finite set of points. In this talk, after a preliminary recall of the definition and the main features of Schr ödinger operators with point interactions, I will discuss some recent results on their scattering and smoothing properties. I will also discuss the characterization of the Sobolev norms induced by such operators. Based on joint works with G. Dell'Antonio, V. Georgiev, F. Iandoli, A. Michelangeli, and K.Yajima.

18:30 Luca Oddis (Sapienza Università di Roma)
Quadratic Forms for Two-Anyon Systems
We review the main issues concerning the well-posedness (as suitable self-adjoint operators) of the Hamiltonians of two non interacting anyons, i.e., exotic particles obeying to fractional statistics in two dimensions. We show that such operators can be identified with a one-parameter family of self-adjoint extensions of a suitable symmetric operator with Aharonov-Bohm-like magnetic potential. We also derive the explicit expressions of the corresponding quadratic forms and prove their closure and boundedness from below. Joint work in progress with M. Correggi.

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