Notiziario Scientifico
Notiziario dei Seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 22 al 28 febbraio 2016
Lunedì 22 febbraio 2016
Ore 11:00, aula B
Incontro di lavoro su Calcolo delle Variazioni e Γ-convergenza/
Working seminar on Calculus of Variations and Γ-convergence
Roberto Alicandro (Università di Cassino)
Interactions beyond nearest neighbours and rigidity of
discrete energies: some results and open problems.
I will analyse the rigidity of discrete energies where at least nearest
and next-to-nearest neighbour interactions are taken into account.
My purpose is to examine the role of interactions beyond nearest neighbours
in penalising changes of orientation and how, to some extent, they may
replace the positive-determinant constraint that is usually required when
only nearest neighbours are accounted for. Following the same approach,
I will also present the asymptotic analysis of a discrete model for nanowires.
Lunedì 22 febbraio 2016
Ore 11:00, aula 311, Università di Roma Tre,
largo san L. Murialdo 1
Minicorso di Geometria
Olivier Lorscheid (IMPA, Rio de Janeiro)
Scheme theoretic tropicalization I
After Kajiwara and Payne's works in the late 2000's, it was well-understood
how to tropicalize a closed subvariety of a toric variety. In recent years,
this process got generalized in different direcetions. While Jeff and Noah
Giansiracusa enhanced tropical varieties with an underlying scheme structure,
employing the theory of so-called semiring schemes, Thuillier and Ulirsch
replaced the ambient toric variety by toroidal embeddings, or more general,
a log structure. In this series of three lectures, we will show how all of
these theories can be understood on a common basis by using the language of
so-called blueprints. After reviewing the above mentioned concepts, we will
introduce bluprints and blue schemes. We redefine the tropicalization of a
variety as the solution to a certain moduli problem and consruct the
corresponding moduli space under some ambient hypothesis. Finally, we
show how to recover the above mentioned theories within the languange
of blue schemes.
Lunedì 22 febbraio 2016
Ore 14:30, aula di Consiglio
Seminario di Analisi Matematica
Carlo Nitsch (Università di Napoli Federico II)
Rottura di simmetria in un problema di isolamento termico
Considereremo il problema di massimizzare l'isolamento termico di un
assegnato dominio Ω avendo a disposizione una massa assegnata di
isolante da disporre lungo la sua frontiera.
In particolare il comportamento a lungo termine della temperatura è
legato ad un problema agli autovalori di un operatore differenziale.
Sorprendentemente il problema presenta una rottura di simmetria nel senso
che, nel caso in cui Ω sia una palla e la quantità di isolante
a disposizione è sotto una certa soglia, la disposizione migliore
non è quella simmetrica.
Martedì 23 febbraio 2016
Ore 10:30, aula 311, Università di Roma Tre,
largo san L. Murialdo 1
Minicorso di Geometria
Olivier Lorscheid (IMPA, Rio de Janeiro)
Scheme theoretic tropicalization II
Martedì 23 febbraio 2016
Ore 11:00, aula di Consiglio
Esame finale di dottorato
Roberto Feola (Sapienza Università di Roma)
Quasi-periodic solutions for fully nonlinear NLS
Mercoledì 24 febbraio 2016
Ore 14:30, aula di Consiglio
Seminario di Algebra e Geoetria
Oliver Lorscheid (IMPA)
Quiver Grassmannians of extended Dynkin type D
Since cluster algebras have been introduced in the early 2000's,
they receive growing attention from researchers in representation
theory and other other areas of mathematics and physics.
A fundamental problem in this subject are explicit descriptions
of cluster algebras in terms of generators and relations.
While cluster algebras of extended Dynkin type A are well-understood,
there are only partial results for type D. In collaboration with
Thorsten Weist, we have established formulas for the Euler
characteristics of the associated quiver Grassmannians, which
leads to explicit formulas for the cluster variables in terms
of the initial cluster variables.
In this talk, we will give an overview over the methods that
entered the lengthy proof of these formulas. The central result
of this work is that all quiver Grassmannians of extended Dynkin
type admit decompositions into affine spaces.
Mercoledì 24 febbraio 2016
Ore 16:00, aula F, Università di Roma Tre,
largo san L. Murialdo 1
Colloquium di Matematica
Carlangelo Liverani (Università di Roma Tor Vergata)
Fast-slow deterministic systems: beyond averaging
Problems with a time scale separation (that is: some features evolve
much faster than others) appear naturally in many fields of physics
and mathematics. In such situations one can often apply some form of
averaging theory which implies that, in the limit of infinite time
scale separation, the slow variables, properly rescaled, evolve
according to an effective autonomous equation.
Unfortunately, in reality one has a fixed, not infinite, scale
separation. Moreover, one may be interested in times much longer than
the ones to which averaging applies. Thus the natural question: is it
possible to go beyond averaging?
I will describe how this can be done in a very simple (but highly non
trivial) example. In so doing, I will illustrate precisely how random
behaviour might appear in a completely deterministic system and how it
might lead to metastability phenomena.
Giovedì 25 febbraio 2016
Ore 10:30, aula 311, Università di Roma Tre,
largo san L. Murialdo 1
Minicorso di Geometria
Olivier Lorscheid (IMPA, Rio de Janeiro)
Scheme theoretic tropicalization III
Giovedì 25 febbraio 2016
Ore 14:30, aula 211, Università di Roma Tre,
largo san L. Murialdo 1
Seminario di Geometria
Cecilia Salgado (Universidade Federal de Rio de Janeiro)
Classification of elliptic fibrations on certain K3 surfaces
Let X be an algebraic K3 surface endowed with a non-symplectic involution.
We classify all elliptic fibrations on X under some hypothesis on the
non-symplectic involution. The idea behind it involves transferring the
classification problem to a 'simpler' surface from the geometric point
of view. This is work in progress with Alice Garbagnati (Milano).
Venerdì 26 febbraio 2016
Ore 12:00, aula di Consiglio
Seminari MoMa
Anna Tramontano (Sapienza Università di Roma)
The ultimate mystery is ourselves: the fascinating challenge
of computational biology
The computational analysis and interpretation of the wealth of
biological data that is being produced every day is a cogent
problem in the life sciences. The task can be mapped to an
engineering project were we need to have the parts list, understand
their tolerance thresholds, find the assembly instruction and,
finally, simulate its behaviour.
Determining the identity and function of all of the sequence elements
in human DNA is a daunting challenge that can be approached with
various techniques, mainly based on statistics and evolutionary
considerations. The next challenge is to correlate variations in the
genes and the insurgence of diseases: the human variation data are
accumulating with unprecedented speed and they need to be interpreted
in order to open the road to their use in medical settings.
The assembly of the biological elements, for example, protein-protein
interactions are at the basis of most cellular processes and crucial
for many bio-technological applications. During the last few years the
development of high-throughput technologies has produced several
large-scale protein-interaction data sets for various organisms.
It is important to develop tools for dissecting their content and
analyse the information they contain using data-integration and
computational methods. Finally, one would like to simulate the
behaviour of whole cells or even whole organs. This area of research
is still at its infancy, but it is important to pursue its goals, even
with limited and incomplete data.
In our discussion, I will outline which are the main challenges in
pursuing the fascinating goal of understanding life at the molecular level.
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