Notiziario Scientifico
Notiziario dei Seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 26 settembre al 2 ottobre 2016
Lunedì 26 settembre 2016
Ore 14:30, aula di Consiglio
seminario di Analisi Matematica
Masayasu Mimura (Meiji University, Tokyo)
How farmers spread into a region occupied by hunter-gatherers?
-The Neolithic transition of populations in Europe-
Martedì 27 settembre 2016
Ore 14:30, aula 311, Università di Roma Tre, l.go san L. Murialdo 1
seminario di Fisica Matematica
Alessandro Olgiati (SISSA, Trieste)
Effective dynamics for multiple coupled Bose-Einstein condensates
I will present a rigorous derivation of the effective equations for the many-body quantum
dynamics of a system consisting of different species of identical bosons (a so-called
multi-component Bose-Einstein condensate). In the limit of large system, the
dynamics is well approximated by coupled nonlinear Schrödinger equations, one
for each single-particle orbital of the BEC. The technique is based on a suitable
adaptation of Peter Pickl's counting method, which I will introduce; a quantitative
estimate for the error is also provided, in terms of the number of particles for each
species. I will discuss both the cases of mean-field and Gross-Pitaevskii regimes.
Mercoledì 28 settembre 2016
Ore 14:30, aula INdAM
seminario
J. Frohlich (ETH Zurich)
Operator algebras and the foundations of quantum mechanics
I review a novel approach to the quantum theory of events and observations.
After an introduction to this subject, I introduce a precise notion of events and sketch
the theory of direct (projective) observations. An essential element of this theory is a
basic principle of 'loss of access to information', which I will discuss in some detail.
The theory highlights the fundamental irreversibility of the time-evolution of states in
quantum mechanics; ('ETH approach to Quantum Mechanics). I conclude with a sketch
of the theory of indrect (Kraus) measurements and a discussion of examples.
Mercoledì 28 settembre 2016
Ore 15:00, aula G
seminario di Storia e Didattica della Matematica
Anna Sfard (University of Haifa and Visiting Professor Sapienza)
On the need for theory of mathematics learning and the promise of discursive
approaches
In this talk, research in mathematics education is defined as a special type of discourse
in which potentially useful stories about learning and teaching mathematics are being told.
A consistent collection of stories coming from a given discourse is known as a theory.
A 'commognitive' version of theory of mathematics learning, a representative example of
discursive approach made distinct by its foundational assumption about the unity of
thinking and communicating, is then presented in accord with this discursive definition.
Mercoledì 28 settembre 2016
Ore 16:00, aula di Consiglio
seminario di Fisica Matematica
Giambattista Giacomin (Université Paris Diderot)
Dynamical models on random graphs: mean field versus long time behavior
I will address the issue of the proximity of interacting diffusion models on large graphs
with a uniform degree property and the corresponding mean field model, i.e. a model
on the complete graph with a suitably renormalized interaction parameter.
Examples include Erdos-Renyi graphs with edge probability p(n), n is the number of vertices,
such that p(n)n tends to infinity as n does. I will present a general result establishing this
proximity on finite time horizon, by exploiting the fact that both systems are accurately
described by a Fokker-Planck PDE in the limit. I will then try to put this result into
perspective by discussing the limitations of our approach.
Mercoledì 28 settembre 2016
Ore 16:00, aula 311, Università di Roma Tre, l.go san L. Murialdo 1
seminario di Analisi Matematica
Massimiliano Berti (SISSA, Trieste)
Almost global existence of periodic capillarity-gravity waves
We present long time existence results for the solutions of gravity-capillary water
waves equations with small initial periodic data. The proof is based on a paradifferential
reduction of the equations and a Birkhoff normal form analysis.
Joint work with J.M. Delort.
Giovedì 29 settembre 2016
Ore 14:15, aula B
corso di Dottorato
Valerio Toledano Laredo (Northeastern University, Boston)
Differential equations and quantum groups , I
The goal of this course is to explain how quantum groups are natural
receptacles for the monodromy of a class of Fuchsian differential
equations associated to complex, semisimple Lie algebras known
as the Knizhnik-Zamolodchikov and Casimir connections.
A more detailed description of the course is available at the following
link.
Venerdì 30 settembre 2016
Ore 11:00, aula Majorana (edificico Marconi), dipartimento di Fisica
seminario
Alessandro Pizzo (Università di Roma Tor Vergata)
Bose particles in a box: a convergent expansion of the ground in the
mean field limiting regime
I shall report on a novel multi-scale technique to study many-body quantum systems where
the total number of particles is kept fixed. The method is based on Feshbach-Schur map and
the scales are represented by occupation numbers of particle states.
First, I consider a three-modes (including the zero mode) Bogoliubov Hamiltonian for a
sufficiently small ratio between the kinetic energy and the Fourier component of the
(positive type) potential corresponding to the two nonzero modes.
For any space dimension d (d≥ 1) and in the mean field limiting regime (i.e., at fixed box
volume |Λ| and for a number of particles, N, sufficiently large) this method provides
the construction of the ground state and its expansion in terms of the bare operators that
in the limit N goes to ∞ is up to any desired precision.
In space dimension d≥ 3 the method provides similar results for an arbitrarily large (finite)
box and a large but fixed particle density ρ, i.e., ρ is independent of the size of
the box. Then, I'll show how this method can be extended to finitely many modes (i.e., particles
in a finite box, and u.v. cut-off imposed on the two-body potential) interacting according to
the complete Hamiltonian in the mean field limiting regime.
N.B. questo seminario sostituisce la sesta lezione del minicorso di J. Frohlich (ETH Zurich)
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esclusivamente all'indirizzo di posta elettronica
seminari@mat.uniroma1.it
entro le ore 24 del giovedì precedente la settimana interessata.
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