Notiziario Scientifico
Notiziario dei Seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 15 al 21 febbraio 2016
Lunedì 15 febbraio 2016
Ore 14:30, aula di Consiglio
Seminario di Analisi Matematica
Giuseppe Mingione (Università di Parma)
Recenti sviluppi in teoria del potenziale non lineare
La classica teoria del potenziale tratta delle proprietà fini
delle funzioni armoniche e delle soluzioni di equazioni ellittiche
lineari. Negli ultimi anni si è sviluppata una teoria parallela,
non lineare, di cui darò qualche assaggio.
Martedì 16 febbraio 2016
Ore 10:30, aula riunioni (primo piano), IAC, via dei Taurini 19
Seminario di Matematica Applicata
Monika Twarogowska (Università de L'Aquila)
Numerical analysis of the traveling waves emerging in a kinetic
model of chemotaxis
We investigate numerically a one-dimensional linear kinetic equation derived
from a velocity jump process modeling bacterial chemotaxis in presence of a
chemical signal, produced by cells, and nutrient present in the environment.
The model was used to describe accurately lab experiments, in which bands of
bacteria are moving across a micro-channel at constant speed. The problem is
very different from classical reaction-diffusion traveling waves, as biased
transport is the dominant effect here. Calvez et al. obtained analytic
results on the existence of traveling waves in the diffusive limit of the
velocity-jump process with temporal sensing. The kinetic part of the system
is approximated by the well-balanced scheme with the time-space dependent
scattering matrix containing coupling with the parabolic system for the
concentrations of the chemoattractants. The method gives an accurate
resolution in the velocity field and we compare it with the classical
time-splitting approach. Then we study numerically the formation and
stability of the traveling waves emerging in the kinetic model.
Finally, we consider a discrete velocity field and show some sets of parameters
for which there exists a numerical cont-example to the existence and stability
of traveling waves.
Martedì 16 febbraio 2016
Ore 12:00, aula 207, LUISS Guido Carli, viale Romania 32
Decision science community seminar @ LUISS
Matias Nunez (Université Paris Dauphine)
Unanimous Implementation: A Case for Approval Mechanisms
We consider a class of indirect mechanisms, the Approval ones, in
which the players' strategies coincide with the subsets of the outcome
space. We focus on the single-peaked domain and we prove that:
a) each of these rules is characterized by a unique equilibrium outcome and
b) for every strategy-proof single-peaked rule there exists an Approval one
that unanimously implements it. That is, Approval rules fix the problem of
equilibrium-outcome multiplicity that is inherent to the ensuing games of
strategy-proof single-peaked rules and, perhaps more importantly, promote
social coherence: the implemented outcome is approved by every player.
Martedì 16 febbraio 2016
Ore 15:00, aula di Consiglio
Seminario di Modellistica Differenziale Numerica
Marco Castellano (INAF)
Astrofisica osservativa e metodi matematici per l'analisi di immagini
Lo studio di immagini digitali del cielo è uno dei mezzi fondamentali
dell'astrofisica e cosmologia odierne. Il seminario presenterà innanzitutto
gli scopi e le specificità delle immagini astronomiche e le problematiche
legate alla necessità di un'analisi quantitativa volta a determinare le
proprietà fisiche degli oggetti celesti. Verranno discusse le tecniche di
analisi (manipolazione, segmentazione, fotometria) maggiormente in uso e le
potenzialità nel contesto astronomico di algoritmi di super-risoluzione,
structure-texture decomposition e segmentazione.
Martedì 19 febbraio 2016
Ore 16:00, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Analisi Complessa
Finnur Larusson (University of Adelaide)
The Oka principle in geometric invariant theory
Grauert proved in 1958 that every continuous section of a holomorphic
principal G-bundle over a Stein space can be deformed to a holomorphic section.
Here, G is any complex Lie group. Starting with Gromov's seminal paper in 1989,
Grauert's theorem has been extended to much more general bundles. I will describe
recent joint work with Frank Kutzschebauch (Bern) and Gerald Schwarz (Brandeis)
in which we adapt Grauert's theorem to certain 'bundles' that arise naturally in
geometric invariant theory but can be badly singular. This work has applications to
the so-called linearisation problem for group actions on affine spaces. I
will give plenty of background; in particular, I will not assume any familiarity with
geometric invariant theory.
Mercoledì 17 febbraio 2016
Ore 14:30, aula di Consiglio
Seminario di Algebra e Geometria
Paolo Stellari (Milano Statale)
Uniqueness of dg enhancements in geometric
contexts and Fourier-Mukai functors
The quest for a (possibly unique) lift of exact functors and
triangulated categories to dg analogues is highly non-trivial
and rich of subtle aspects, already in geometric contexts.
This is made clear by the most recent developments concerning
Fourier-Mukai functors, which will be reviewed in this talk.
On the other hand, it was a general belief and a formal conjecture
by Bondal, Larsen and Lunts that the dg enhancement of the bounded
derived category of coherent sheaves or the category of perfect
complexes on a (quasi-)projective scheme is unique.
This was proved by Lunts and Orlov in a seminal paper.
In this talk we will explain how to extend Lunts-Orlov's results to
several interesting geometric contexts. Namely, we care about the
category of perfect complexes on noetherian separated schemes with
enough locally free sheaves and the derived category of quasi-coherent
sheaves on any scheme. This is a joint work with A. Canonaco.
Mercoledì 17 febbraio 2016
Ore 15:00, aula Picone
Seminario sulla Storia della Facoltà
Enrico Rogora (Sapienza Università di Roma)
Le chiamate di Enriques e Severi: Roma diviene il centro del mondo
per la geometria algebrica
Alla morte di Alberto Tonelli, il 29 Dicembre 1920, restano scoperte, presso
la Facoltà di Scienze di Roma, le cattedre di Algebra e di Calcolo.
Per la loro copertura si scatena una battaglia tra Volterra, che vuole
chiamare Leonida Tonelli e Levi Civita e i geometri, che vogliono Federigo
Enriques e Francesco Severi. L'esito della battaglia, di cui seguiremo lo
svolgersi e i retroscena attraverso i verbali dei Consigli di Facoltà
e le lettere tra alcuni dei protagonisti, segnerà l'inizio del declino
della leadership di Volterra nella comunità dei matematici e l'ascesa
prepotente di quella di Severi.
Mercoledì 17 febbraio 2016
Ore 15:00, aula Dal Passo, Università di Roma Tor Vergata
Colloquium Levi-Civita
Sergio Doplicher (Sapienza Università di Roma)
Quantum Physics, Quantum Spacetime and Quantum Geometry
The features of Quantum Mechanics which were new for Classical Physics,
and still are definitely counter - intuitive, can all be summarized in a
statement: the C* Algebra generated by all observables is non-commutative.
In Quantum Field Theory, neglecting gravitational forces between elementary
particles, observables measured in spacelike separate regions commute, which
makes the overall C* algebra 'more non-commutative'. But spacetime regions
are subset of Minkowski space (or of a curved Einstein manifold), a classical
space. But if we do not neglect gravity among the interactions between
elementary particles, spacetime cannot be described by a classical manifold
in the small. It becomes a Quantum Space. We will review a simple model of
Quantum Spacetime, the spectral properties of some of its geometric operators,
the problem of interacting quantum fields on quantum spacetime, and close with
few words on the cosmological consequences of the model
Mercoledì 17 febbraio 2016
Ore 16:00, aula B
Corso di dottorato
Giovanni Cerulli Irelli (Sapienza Università di Roma)
Grassmanniane quiver I
Giovedì 18 febbraio 2016
Ore 14:30, aula 211, Università di Roma Tre,
largo san L. Murialdo 1
Seminario di Geometria
Giulio Codogni (Università di Roma Tre)
Torus equivariant K-stability
We prove (using algebro-geometric methods) two results that allow to test the
positivity of the Donaldson-Futaki weights of arbitrary polarised varieties
via test-configurations which are equivariant with respect to a maximal torus
in the automorphism group. It follows in particular that there is a purely
algebro-geometric proof of the K-stability of projective spaces (or more
generally of smooth toric Fanos with vanishing Futaki character, as well
as of the examples of non-toric Kahler-Einstein Fano threefolds due to Ilten
and Suss) and that K-stability for toric polarised manifolds can be tested
via toric test-configurations. A further application is a proof of the
K-stability of constant scalar curvature polarised manifolds with continuous
automorphisms. Our approach is based on the method of filtrations introduced
by Wytt Nystrom and Szekelyhidi and indeed many of our relts also extend to
the class of (not necessarily finitely generated) polynomial filtrations.
This is a joint work with J. Stoppa.
Venerdì 19 febbraio 2016
Ore 16:00, aula D'Antoni, Università di Roma Tor Vergata
Seminario
Sebastiano Carpi (Università di Chieti-Pescara)
Loop groups and noncommutative geometry
We describe the representation theory of loop groups in terms of K-theory
and noncommutative geometry. This is done by constructing suitable spectral
triples associated with the level l projective unitary positive-energy
representations of any given loop group LG. The construction is based on
certain supersymmetric conformal field theory models associated with LG.
The construction can be generalized, in the setting of conformal nets, to
many other rational chiral conformal field theory models including coset
models and the moonshine conformal net.
(Based on a joint work with Robin Hillier)
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