Notiziario Scientifico
Notiziario dei Seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 12 al 18 dicembre 2016
Lunedì 12 dicembre 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
Andrea Braides (Università di Roma Tor Vergata)
A damage model as a result of the interaction between elasticity and fracture
We examine a simple model of discrete interactions by Novak and Truskinovsky
mixing elastic and Lennard-Jones potentials. We derive a continuum (semidiscrete)
counterpart depending on a small parameter corresponding to the interatomic distance
and compute its behaviour as this parameter tends to 0. The resulting energy is
of 'damage type'. We compare the limit with that of Novak and Truskinovsky highlighting
differences between the discrete and the semidiscrete formulation.
(work in progress with A. Causin and M. Solci)
Martedì 13 dicembre 2016
Ore 13:45, aula 1200, Università di Roma Tor Vergata
seminario di Geometria Algebrica
Thomas Dedieu
Enumerazione di curve in superficie toriche mediante geometria tropicale
secondo Mikhalkin e Brugallé, III
Martedì 13 dicembre 2016
Ore 14:30, aula D'Antoni, Università di Roma Tor Vergata
seminario di Equazioni Differenziali
Federica Sani (Università di Milano)
Higher order Adams'inequality with the exact growth condition
Adams'inequality is the complete generalization of the Trudinger-Moser inequality
to the case of Sobolev spaces involving higher order derivatives and the Trudinger-Moser
inequality is a substitute for the the well known Sobolev embedding Theorem when
the limiting case is considered. We first discuss the optimal growth rate of the
exponential-type function in Trudinger-Moser inequalities when the problem
is considered in the whole space RN. Next, we extend this
result in the higher order case.
Martedì 13 dicembre 2016
Ore 15:00, aula di Consiglio
seminario di Modellistica Differenziale Numerica
Elena Agliari (Sapienza Università di Roma)
Analytical and numerical approaches to study free energy minima of associative
recurrent neural networks
Since the seminal works by Hebb and Pavlov (in neurophysiology) and by McCulloch, Pitts
and Rosenblatt (in the electronic counterpart), the principles behind brain's information
processing have inspired mathematicians and engineers in designing adaptive softwares
and artificial information processing systems.
In particular, the cortical modules of mammal's brain exhibit 'associative memory',
namely the ability to reconstruct the whole information regarding a learned pattern,
when supplied by only partial data on the learned pattern.
This is a cooperative feature, arising from the mutual and complex interaction of a large
number of elementary neurons (order of 10^10) and can thus be nicely described by a
class of statistical-mechanics disordered models termed 'associative neural networks'.
In this talk we will review the paradigmatic Hopfield model and some approaches used
for the investigation of its properties.
Mercoledì 14 dicembre 2016
Ore 14:30, aula di Consiglio
seminario di Algebra e Geometria
Sara Perna (Sapienza)
Siegel modular forms: some geometric applications
In this talk I will present some of the results of my Ph.D. thesis. I will show some geometric
applications of the theory of Siegel modular forms. The first result I will present is a
generalization of Mukai's result about the existence of a degree 8 automorphism of the
Igusa quartic, a compactification of a moduli space of principally polarized abelian varieties
with some extra structure.
Although I will mostly talk about Siegel modular forms as tools for the study of complex
abelian varieties and their moduli spaces, they also represent an interesting and rich
subject by themselves in the theory of automorphic forms. Indeed I will give a new
construction of vector-valued modular forms from scalar-valued ones involving some
multi-linear algebra constructions. As an application I will show the identity of two
remarkable spaces of vector-valued modular forms. Finally I will give a new characterization
of the locus of decomposable principally polarized abelian varieties through the image of the
smooth 2-torsion points on the theta divisor.
Mercoledì 14 dicembre 2016
Ore 15:00, aula di Consiglio
seminario di Algebra e Geometria
Paolo Arcangeli (Sapienza)
A Camacho-Sad-type index theorem for a couple of holomorphic self-maps
Let M be a n-dimensional complex manifold and f,g two distinct holomorphic self-maps of M.
Suppose that f and g coincide on a globally irreducible compact hypersurface S of M. If one of
the two maps is a local biholomorphism in a neighborhood of the regular part S' of S and, if
needed, S' sits into M in a particular nice way, then it is possible to define a 1-dimensional
holomorphic (possibly singular) foliation on S' and a partial holomorphic connection on the
normal bundle of S' in M.
As a consequence, one can localize the n-1 power of the first Chern class of the line bundle
[S] on M canonically induced by S and thus get an index theorem.
Mercoledì 14 dicembre 2016
Ore 16:30, aula III
seminario di Dipartimento Matematica e Società
Francesco Sylos Labini (CNR-ISC Roma)
Rischio e previsione: cosa può dirci la scienza sulla crisi
La crisi economica sta cambiando la struttura della nostra società,
introducendo disuguaglianze insormontabili, marginalizzando le energie più
giovani, soffocando la ricerca scientifica e così inibendo anche la possibilità
di sviluppare quelle idee e innovazioni che potrebbero contribuire a guidarci fuori dalla
crisi stessa. La scienza può fornire degli strumenti chiave utili non solo per
comprendere i problemi della nostra epoca ma anche per tracciare delle prospettive
che possono rappresentare una solida e valida alternativa alla dilagante legge del
più forte - un malinteso darwinismo sociale - oggi in auge.
In particolare le idee sviluppate nell'ultimo secolo nell'ambito delle scienze naturali
giocano un ruolo chiave per la comprensione di molti problemi, apparentemente
diversi e non connessi, alla radice della crisi attuale e possono suggerire soluzioni
plausibili e originali.
Bibliografia: Francesco Sylos Labini 'Rischio e previsione', Editori Laterza, 2015.
Venerdì 16 dicembre 2016
Ore 11:30, Biblioteca - sala Ingegneria Geotecnica, Dipartimento di Ingegneria
Strutturale e Geotecnica, via Eudossiana 18
seminario
Antonio de Simone (SISSA, Trieste)
Shape control in bio-inspired motility at microscopic scales
Venerdì 16 dicembre 2016
Ore 14:30, aula Riunioni (primo pIano), IAC-CNR, via dei Taurini 19
seminario di Matematica Applicata
Michele di Pierro (Center for Theoretical Biological Physics, Rice University, Houston)
The Architecture of Interphase Chromosomes and its Epigenetic Regulation
Chromatin consists of DNA and hundreds of proteins that interact with the genetic material.
In vivo, chromatin folds into nonrandom structures. The physical mechanism leading to
these characteristic conformations, however, remains poorly understood. We recently
introduced MiChroM [1], a model that generates chromosome conformations by using
the idea that chromatin can be subdivided into types based on its biochemical interactions.
Here we extend and complete our previous finding by showing that structural chromatin
types can be inferred from ChIP-Seq data. Chromatin types, which are distinct from DNA
sequence, are partially epigenetically controlled and change during cell differentiation,
thus constituting a link between epigenetics, chromosomal organization, and cell
development. We show that, for GM12878 lymphoblastoid cells we are able to predict
accurate chromosome structures with the only input of genomic data. The degree of
accuracy achieved by our prediction supports the viability of the proposed physical
mechanism of chromatin folding and makes the computational model a powerful tool
for future investigations.
[1] M. Di Pierro, et al. ; Transferable model for chromosome architecture; PNAS 2016 113 (43).
[2] Commentary by G. Gursoy and J. Liang; PNAS 2016 113 (43).
Venerdì 16 dicembre 2016
Ore 16:00, aula Picone
seminario per insegnanti (Piano Lauree Scientifiche)
Michela Barsanti (liceo Vittorio Colonna Roma)
Guido Cavallaro (Sapienza Università di Roma),
Alberto De Sole ( Sapienza Università di Roma)
Numeri primi: aspetti teorici e didattici
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