a cura del Dipartimento di Matematica

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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