Notiziario Scientifico
Notiziario dei seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 13 al 19 novembre 2017
Lunedì 13 novembre 2017
Ore 14:15, aula di Consiglio
seminario di Equazioni Differenziali
Paolo Marcellini (Università di Firenze)
Some remarks in the Calculus of Variations
I will discuss about some new and old problems of the Calculus of the
Variations. (Hoping that this abstract will take curious some of the participants).
Lunedì 13 novembre 2017
Ore 15:15, aula di Consiglio
seminario di Equazioni Differenziali
Vincent Millot (Université Paris Diderot)
Fractional harmonic maps and local or nonlocal minimal surfaces
In this talk I will present some results concerning fractional harmonic maps into a manifold.
In a first part, I will focus on the case involving the square root Laplacian (originally
introduced by F. Da Lio & T. Riviere) and try to enlighten the analogies with classical
harmonic maps and (local) minimal surfaces. In a second part, I will draw the link between
fractional harmonic maps and the so-called 'nonlocal minimal surfaces' of L. Caffarelli,
J.M. Roquejoffre, & O. Savin, and give some recent regularity results about them.
Martedì 14 novembre 2017
Ore 14:00, aula di Consiglio
seminario di Probabilità
Luca Scarpa (University College London)
Well-posedness of semilinear SPDEs with singular drift: a variational approach
Well-posedness is proved for singular semilinear SPDEs on a smooth bounded domain D in Rn.
The linear part is associated to a coercive linear maximal monotone operator on L^2(D) while the drift
is represented by a multivalued maximal monotone graph everywhere defined on R, on which no growth
nor smoothness conditions are required. Moreover, the noise is given by a cylindrical Wiener process on
a Hilbert space U, with a stochastic integrand taking values in the Hilbert-Schmidt operators from U to
L2(D): classical classical Lipschitz-continuity hypotheses for the diffusion coefficient are
assumed. The proof consists in approximating the equation, finding uniform estimates both pathwise and
in expectation on the approximated solutions, and then passing to the limit using compactness and lower
semicontinuity results. Finally, possible generalizations are discussed. This study is based on a joint
work with Carlo Marinelli (University College London)
Martedì 14 novembre 2017
Ore 14:30, aula Dal Passo, dipartimento di Matematica,
Università di Roma Tor Vergata
seminario di Equazioni Differenziali
Annalisa Massaccesi (Universitat Zurich)
Partial regularity for the hyperdissipative Navier-Stokes equations
In this joint work with Maria Colombo and Camillo De Lellis we prove a space-time partial regularity
result a la Caffarelli-Kohn-Nirenberg for suitable weak solutions of the hyperdissipative Navier-Stokes
equations.
Martedì 14 novembre 2017
Ore 14:30, aula 311, Università di Roma Tre,
largo san Leonardo Murialdo 1
seminario di Fisica Matematica
E. Runa (Max-Planck-Institute for Mathematics in the Sciences, Leipzig)
Exact periodic stripes for minimizers of a local/non-local
interaction functional in general dimension
In this talk we will consider a functional consisting of a perimeter
term and a non-local term which are in competition. In the discrete
setting such functional was introduced by Giuliani, Lebowitz, Lieb and
Seiringer. We show that the minimizers of such functional are optimal
periodic stripes for both the discrete and continuous setting. In the
discrete setting, such behaviour has been shown by Giuliani and
Seiringer using different techniques for a smaller range of exponents.
One striking feature of the functionals is that the minimizers are
invariant under a smaller group of symmetries than the functional
itself. In the continuous setting, to our knowledge this is the first
example of a model with local/nonlocal terms in competition such that
the functional is invariant under permutation of coordinates and the
minimizers display a pattern formation which is one dimensional. This
model has many similarities with the celebrated Ohta-Kawasaki
functional. In particular for Ohta-Kawasaki functional, the minimality
of periodic stripes is conjectured. This work is in collaboration with
Sara Daneri.
Martedì 14 novembre 2017
Ore 14:30, room 207, LUISS 'Guido Carli', viale Romania 32
seminario
Piermarco Cannarsa (Università di Roma Tor Vergata)
Mean Field Games with State Constraints
This talk will address deterministic mean field games for which agents are restricted
inside a closed domain in Euclidean space. In this case, the existence, uniqueness,
and regularity of Nash equilibria cannot be deduced as for unrestricted state space
because, for a large set of initial conditions, the uniqueness of solutions to the
minimization problem which is solved by each agent is no longer guaranteed.
We will attack the problem by considering a relaxed version of it, for which the
existence of equilibria can be proved by set-valued fixed point arguments. We will
then give a uniqueness result for such equilibria under a classical monotonicity
assumption. Finally, we will analyze the regularity of the relaxed solution aiming
to show that it satisfies the first order mean field games system.
Martedì 14 novembre 2017
Ore 15:00, aula di Consiglio
seminario di Modellistica Differenziale Numerica
E. Iacomini (SapienzaUniversità di Roma)
Sensitivity analysis of the LWR model for traffic forecast on large networks using
Wasserstein distance
In this talk we present a sensitivity analysis of a PDE model for traffic forecast on networks.
The analysis is made with respect to the parameters and to the network. In order to compare
different numerical solutions coming from different inputs, we will use the Wasserstein distance,
computed by a suitable numerical method.
Traffic uncertainty is evaluated for different initial data, different fundamental diagrams,
different vehicle distributions at junctions and different network sizes. Joint work with
M. Briani and E. Cristiani.
Mercoledì 15 novembre 2017
Ore 14:00, aula di Consiglio
seminario
Nils Carqueville (Universitat Wien)
Topological quantum field theories: ADE orbifolds and beyond
Topological quantum field theory is a way of representing structures from topology and
geometry on algebra. In this talk I will review the basic approach, describe a unification
of group orbifolds and state sum constructions, and then discuss applications.
In particular, one finds new relations among simple isolated singularities of ADE type as
well as among the associated Dynkin quivers.
Giovedì 16 novembre 2017
Ore 14:30, aula di Consiglio
seminario PDN P(n)
Dario Mazzoleni (Università Cattolica del Sacro Cuore, Brescia)
Gradient flows for eigenvalues of potentials
In the first part of the talk we will discuss the difficulties when
trying to make shape flows for spectral shape optimization problems
involving eigenvalues of the Dirichlet Laplacian, stressing the issue
of finding a good topology for shapes.
In fact, even relaxing the shapes to capacitary measures, which is a
standard procedure in shape optimization, does not seem to give
satisfying results.
The second part of the talk will focus on the study of a gradient flow
equation for eigenvalues of potentials, that is, we consider
eigenvalues on absolutely continuous measures with respect to the
usual Lebesgue measure.
In particular, when the functional is the first eigenvalue, we show
that the curves of potentials arising from a minimizing movements
scheme comply with a generalized gradient flow equation.
This is a joint project with Giuseppe Savaré (Pavia).
Venerdì 17 novembre 2017
Ore 11:00, aula seminari (sesto piano), IAC-CNR, via dei Taurini 19
seminario di Matematica Applicata
Michele di Pierro (Rice University)
De Novo Prediction of Human Chromosome Structures: Epigenetic Marking Patterns
Encode Genome Architecture
Inside the cell nucleus, genomes fold into organized structures that are characteristic of cell type.
Here, we show that this chromatin architecture can be predicted de novo using epigenetic data derived
from ChIP-Seq. We exploit the idea that chromosomes encode a one-dimensional sequence of chromatin
structural types. Interactions between these chromatin types determine the three-dimensional (3D)
structural ensemble of chromosomes through a process similar to phase separation. First, a recurrent
neural network is used to infer the relation between the epigenetic marks present at a locus, as
assayed by ChIP-Seq, and the genomic compartment in which those loci reside, as measured by DNA-DNA
proximity ligation (Hi-C). Next, types inferred from this neural network are used as an input to an
energy landscape model for chromatin organization (MiChroM) in order to generate an ensemble of 3D
chromosome conformations. After training the model, dubbed MEGABASE (Maximum Entropy Genomic Annotation
from Biomarkers Associated to Structural Ensembles), on odd numbered chromosomes, we predict the
chromatin type sequences and the subsequent 3D conformational ensembles for the even chromosomes.
We validate these structural ensembles by using ChIP-Seq tracks alone to predict Hi-C maps as well
as distances measured using 3D FISH experiments. Both sets of experiments support the hypothesis of
phase separation being the driving process behind compartmentalization. These findings strongly suggest
that epigenetic marking patterns encode sufficient information to determine the global architecture
of chromosomes and that de novo structure prediction for whole genomes may be increasingly possible.
Venerdì 17 novembre 2017
Ore 14:30, aula Dal Passo, dipartimento di Matematica,
Università di Roma Tor Vergata
seminario
Michael Ehrig (University of Sydney)
Functoriality of link homologies and higher representation theory
In this talk, we will discuss the notion of functoriality of
link homologies defined by Khovanov and Khovanov-Rozansky. These link
homologies are categorifications of the link invariants defined by
Reshetikhin-Turaev in case of the special linear group. We will discuss
why functoriality is an important notion and how to show it. The latter
will include the equivariant geometry of Grassmannians and partial flag
varieties as well as higher representation theory.
Venerdì 17 novembre 2017
Ore 16:00, aula Picone
seminario per insegnanti (Piano Lauree Scientifiche)
Claudio Bernardi (Sapienza Università di Roma), Lorenzo Mazza
(Liceo Avogadro, Roma), Antonio Veredice (Liceo Peano, Monterotondo)
Trasformazioni geometriche e teoremi di geometria euclidea
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