Notiziario Scientifico
Notiziario dei Seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 7 al 13 novembre 2016
Lunedì 7 novembre 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
A. Braides (Università di Roma Tor Vergata)
Quasiconvex functions from constrained Dirichlet energies
We consider p-Dirichlet energies from a two-dimensional set into an oscillating
two-dimensional manifold. We show that for p<2 we obtain an effective (homogenized)
energy of p-growth finite in the whole Sobolev space W1,p. For p>2 the
energy density is quasiconvex and infinite on rank-two matrices. An open problem
is whether the energy density, as depending on p, is continuous or not at the transition
exponent p=2, which would be interesting in either cases.
Ongoing work with J. Kristensen.
Lunedì 7 novembre 2016
Ore 14:30, aula di Consiglio
seminario di Analisi Matematica
Albert Fathi (ENS Lyon)
Topology of the set of singularities of viscosity solutions of the
Hamilton-Jacobi equation
This is a joint work with Piermarco Cannarsa and Wei Cheng.
We study the properties of the set S of non-differentiable points of viscosity solutions of
the Hamilton-Jacobi equation, for a Tonelli Hamiltonian.
The main surprise is the fact that this set is locally arc connected-it is even locally
contractible. This last property is far from generic in the class of semi-concave functions.
We also 'identify' the connected component of this set S. This work relies on the idea of
Cannarsa and Cheng to use the positive Lax-Oleinik operator to construct a global propagation
of singularities (without necessarily obtaining uniqueness of the propagation).
Lunedì 7 novembre 2016
Ore 14:30, aula 311, Università di Roma Tre, l.go san L. Murialdo 1
seminario di Analisi Matematica
Matthew He (Nova Southeastern University, Ft. Lauderdale)
Synergy between Biology and Mathematics: past, present, and future
The outline of this talk includes three phases of the synergy between biology and mathematics:
1. The Past: The Motion of the Heart and Blood in Animals (Harvey 1847), Discovery of Genes
(Mendel 1866), Biological Problems that Stimulated Mathematics, Ten Equations that Changed Biology.
2. The Present: The Landscapes of Biological Sciences, The Landscapes of Applied Mathematics, The
Landscapes of Research in Biology and Mathematics, Bioinformatics of Mathematics: Theory, Methods,
and Applications
3. The Future: Potential Problems, Meeting the Challenges: Education Across the Biological, Mathematical
and Computer Sciences, A New Biology Curriculum for the 21st Century, Ten Challenges in the Synergy
Between Biology and Mathematics.
Lunedì 7 novembre 2016
Ore 16:00, aula C
seminario BSD
Simone Diverio (Sapienza Università di Roma)
Elementi di geometria hermitana e kaehleriana
Lunedì 7 novembre 2016
Ore 16:00, aula D'Antoni, Università di Roma Tor Vergata
seminario di Analisi Complessa
Adriano Tomassini (Università di Parma)
Coomologia di varietà complesse e deformazioni
Martedì 8 novembre 2016
Ore 14:00, aula di Consiglio
seminario di Probabilità e Statistica Matematica
Pham Thi Da Cam (Université de Tours)
The survival probability of a critical multi-type branching process
in i.i.d. random environment
We consider Galton Watson branching processes of unique type and multi-type in fixed
and in random environment. The main target is to observe the asymptotic behaviour of
the survival probability of the population. In particular, we utilise the generating
function method thanks to the recursive structure of the process in deterministic
case and condition to the generating function of offspring distribution in random case.
Martedì 8 novembre 2016
Ore 14:30, aula Dal Passo, Università di Roma Tor Vergata
seminario di Equazioni Differenziali
Antonio Siconolfi (Sapienza Università di Roma)
Equazioni di Hamilton-Jacobi su networks
Viene proposta una nuova metodologia per l'analisi di equazioni di Hamilton-Jacobi
su networks. Il punto chiave è di combinare l'equazione differenziale sul
network immerso in uno spazio Euclideo con un'equazione funzionale discreta sui
vertici di un grafo finito associato.
Questa impostazione consente di affrontare in maniera semplice questioni di esistenza
e unicità, nonchè di scrivere formule di rappresentazione nell'ambiente
discreto. Le informazioni sono poi traferite sul network immerso per stabilire, ad
esempio, risultati di regolarità.
Si considereranno equazioni di tipo Iconale e scontato, si formulerà una versione
della teoria KAM debole adattata all'ambiente, e si studierà il comportamento
asintotico delle soluzioni del problema scontato quando il fattore di sconto diventa
infinitesimo. I risultati sono stati ottenuti nell'ambito di una collaborazione con
Alfonso Sorrentino.
Martedì 8 novembre 2016
Ore 15:15, aula di Consiglio
seminario di Modellistica Differenziale Numerica
Roberto Natalini (IAC-CNR)
Some numerical schemes for hyperbolic models of cell movement on networks
We consider a semilinear hyperbolic chemotaxis model in one space
dimension, evolving on a network, with suitable transmission
conditions at nodes. This model is motivated by tissue-engineering
scaffolds used for improving fibroblasts movements in wound healing.
Recently, it has been shown the existence of global (in time) smooth
solutions to this problem for suitably small initial data. Here we
introduce a numerical scheme, which, for zero flux conditions,
guarantees global mass densities conservation. Moreover our scheme is
able to yield a correct approximation of the effects of the source
term at equilibrium and to take into account the contribution of
source terms at nodes. Several numerical tests are presented to show
the behavior of solutions and to discuss the stability and the
accuracy of our approximation. Also, we shall compare our model with
similar parabolic models involving different transmission conditions.
Finally we discuss how this model is able to reproduce some
experiments concerning cells finding the shortest path in a maze.
Mercoledì 9 novembre 2016
Ore 14:00, aula Paoluzzi, Università di Roma Tor Vergata
seminario Teorico
Bergshoeff (Groningen University)
Applied Newton-Cartan Geometry
Mercoledì 9 novembre 2016
Ore 15:00, aula di Consiglio
seminario di Algebra e Geometria
Viveca Erlandsson (Aalto University)
Counting curves on surfaces
Let S be a surface of genus g and r punctures, and c a (not necessarily simple) closed
curve on S. Consider the set of curves in the mapping class group orbit of c. Recently,
Mirzakhani has shown that when S is endowed with a hyperbolic metric, the cardinality
of the subset defined by the curves with length bounded by L is asymptotic to a
constant times L6g-6+2r, as L grows. In this talk we discuss the same problem
but where the length is measured with respect to any Riemannian metric on the surface,
as well as with respect to the word length.
Mercoledì 9 novembre 2016
Ore 15:00, aula Dal Passo, Università di Roma Tor Vergata
colloquium Talk
Valerio Toledano Laredo (Northeastern University, Boston)
Differential equations and quantum groups
Quantum groups were introduced in the mid-eighties by Drinfeld and Jimbo as the algebraic
backbone of the quantum Inverse Scattering Method of Statistical Mechanics. They were soon
found to have a host of other applications: to low-dimension topology, representation theory,
and algebraic geometry to name a few.
This talk will concentrate on one aspect of quantum groups, namely their uncanny ability to
describe the monodromy of integrable systems of partial differential equations attached to
semisimple Lie algebras.
This phenomenon was originally discovered by Drinfeld and Kohno in the early 90s in connection
with the Knizhnik-Zamolodchikov equations of Conformal Theory. More recently, I proved that
quantum groups also describe the monodromy of the so-called Casimir equations of a semisimple
Lie algebra and, in recent joint work with Andrea Appel (USC), that this continues to hold for
any symmetrisable Kac-Moody algebra.
Giovedì 10 novembre 2016
Ore 14:30, aula di Consiglio
seminario P(n)
Lorenzo Brasco (Università di Ferrara)
On some equations with orthotropic structure
We study a variant of the p-Laplacian operator, which arises as the first variation of a
Dirichlet integral with orthotropic structure. The corresponding elliptic equation is much
more degenerate/singular than that for the standard p-Laplacian operator and higher
regularity of solutions appears to be a difficult issue.
We will give some motivations for considering this kind of equations and then present
some regularity results for the gradient of solutions. We will mainly deal with the low
dimensional case. We will also discuss the case of nonstandard growth conditions.
The results presented are contained in some papers written in the last 3 years, in
collaboration with Pierre Bousquet (Toulouse), Guillaume Carlier (Paris Dauphine),
Vesa Julin (Jyvaskyla), Chiara Leone (Napoli), Giovanni Pisante (Caserta) and Anna
Verde (Napoli).
Venerdì 11 novembre 2016
Ore 11:00, Accademia dei Lincei, via della Lungara 10
premio Internazionale Feltrinelli per la Matematica
Jean Bourgain
A journey in a mathematician's world: Fourier analysis, differential equations
and number theory
Venerdì 11 novembre 2016
Ore 12:00, aula di Consiglio
seminario MoMA
Giuliana Indelicato
Nanoparticles under the Mathematical Microscope
Several nanoparticles self-assemble from multiple copies of a limited number of building
blocks, viruses being the archetypal example in biology. A majority of viruses have a highly
ordered protein container (the capsid) that encloses and protects the viral genomic material
from the environment. Understanding the structure of these capsids is fundamental to clarify
how viruses work and possibly how they can be defeated and, to this purpose, a general
classification scheme is needed. For viruses, the theory that identifies the relative
position of the proteins was proposed by Caspar and Klug in the sixties and is still the
current paradigm in the description of capsids.
However, in the last decade scientists have started engineering many different self-assembling
protein nanoparticles. The possible applications are manifold and innovative: from vectors for
the delivery of genes or drugs to synthetic vaccines. The fast development of this research
field poses new challenges for the structural analysis as, in general, synthetic nanoparticles
do not fit into the Caspar and Klug's framework: an original approach is needed to provide
blueprints for the experimental determination of their structure.
We focus on a de novo class of proteins, referred to as self-assembling protein nanoparticles
(SAPNs). This is a family of nanoparticles that provide a versatile platform for synthetic
vaccines against a broad range of diseases, including malaria, SARS, influenza and HIV.
These nanoparticles self assemble from multiple copies of a polypeptide synthesized to
have specific connectivity properties. The polypeptides bind to each other following
precise local assembly rules forming groups of five or three polypeptides. To address the
problem of elucidating the resulting assembled global structure, we use tools from graph
theory. This approach unveils a hidden relation with fullerene geometries and enables a
full classification of the high and low symmetry particles seen in experiments. First and
foremost, this allows to determine the relative distance of the epitopes on the particle
surface and tune the immunogenic effect of the vaccine.
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seminari@mat.uniroma1.it
entro le ore 24 del giovedì precedente la settimana interessata.
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