Notiziario Scientifico
Settimana dal 23 al 29 giugno 2014
Lunedì 23 giugno 2014
Martedì 24 giugno 2014
Martedì 24 giugno 2014
Martedì 24 giugno 2014
Mercoledì 25 giugno 2014
Mercoledì 25 giugno 2014
Mercoledì 25 giugno 2014
Giovedì 26 giugno 2014
Giovedì 26 giugno 2014
Giovedì 26 giugno 2014
Venerdì 27 giugno 2014
Venerdì 27 giugno 2014
Venerdì 27 giugno 2014
Tutte le informazioni relative a questo notiziario devono pervenire
all'indirizzo di posta elettronica
seminari@mat.uniroma1.it
entro le ore 9 del venerdì precedente la settimana di pubblicazione.
Ore 16:30, Aula 1B1, Dipartimento SBAI
Ore 14:00, Aula Picone
Seminario di Probabilità
We study hyperbolic systems of nonlinear PDEs with monotone and bounded data. Without loss of
generality, we assume that these data are cumulative distribution functions (CDFs) on the real line,
and look for solutions that remain so at all time. Such solutions are called 'probabilistic
solutions'. In the scalar case, it is known that the probabilistic solution can be approximated by
the empirical CDF of a system of sticky particles introduced by Brenier and Grenier, that is
described as follows: particles travel on the real line at constant velocity and stick into clusters
at collisions, with conservation of mass and momentum. Stability estimates on the probabilistic
solution in Wasserstein distance were obtained by Bolley, Brenier and Loeper. We introduce a
multitype version of the sticky particle dynamics and use it to obtain the existence of a
probabilistic solution for any choice of data, under a uniformly strict hyperbolicity assumption on
the system. We then derive similar Wasserstein stability estimates. A key ingredient of our proof is
a uniform L^p stability estimate on the evolution of the particle system.
Ore 14:30, Aula 311, Università di Roma III
Seminario di Fisica Matematica
The nonlinear Schrodinger (NLS) equation with spatially dependent nonlinearity describes systems in
which the response of the medium to wave-function propagation is not homogeneous in space. I will
consider a one-dimensional NLS equation in which the nonlinearity is strongly localized in space
around a finite number of points. For suitable scaled, concentrated nonlinearities, I will discuss
the convergence of the dynamics to the one generated by a NLS equation with point-like
nonlinearities. The definition of the limit dynamics is mimicked on the case of a linear point
potential (delta interaction). Nonlinear delta interactions in one and three dimensions, are well
known and extensively studied models in mathematical physics. Our result represents a first attempt
to justify such models in terms of the approximation through regularized dynamics. This is a joint
work in collaboration with D. Finco, D. Noja, and A. Teta.
Ore 14:30, Aula Dal Passo, Università di Roma II
Seminario di Equazioni Differenziali
I will report on recent works related to prescribing a new notion of curvatures, interpolating
somehow between several well-known curvatures. I will discuss several open problems and lines of
research of interest in the field.
Ore 9:30, Aula Picone
9.30 - 10.00 Welcome address
10.00 - 10.40 Masayasu Mimura (Meiji University)
Spatio-temporal oscillations in the Keller-Segel system with logistic growth
10.50 - 11.30 Brian H. Gilding (Kuwait University)
One-dimensional free-boundary problems in inventory control
11.40 - 12.20 Jesus Hernandez (Universidad Autonoma de Madrid)
On linearized stability results for positive solutions to semilinear singular elliptic problems
Ore 14:30, Aula Picone
14.30 - 15.10 Danielle Hilhorst (Universite' Paris-Sud)
On the large time behavior of solutions of a nonlocal evolution equation
15.15 - 15.55 Robert Kersner (University of Pecs)
On a cross-diffusion PDE system
16.30 - 17.10 Corrado Mascia (Sapienza Università di Roma)
Hyperbolic variations of the Allen-Cahn equation
17.15 - 17.55 Adriano Pisante (Sapienza Università di Roma)
Allen-Cahn approximation of mean curvature flow on Riemannian manifolds}
Ore 16:00, Aula Dal Passo, Università di Roma II
Let A be a positive injective operator in a Hilbert space (H, < . , . >), and denote by [ . , . ]
the inner product defined by A: [f,g] = < Af,g > . A closed subspace S â H is called A-compatible if
there exists a closed com- plement for S, which is orthogonal to S with respect to the inner product
[ . , . ]. Equivalently, if there exists a necessarily unique bounded idempo- tent operator Q_S such
that R(Q_S) = S, which is symmetric for this inner product. The compatible Grassmannian Gr_A is the
set of all A-compatible sub- spaces of H. By parametrizing it via the one to one correspondence S <
- > Q_S , this set is shown to be a differentiable submanifold of the Banach space of all bounded
operators in H which are symmetric with respect to the form [ . , . ]. A Banach-Lie group acts
naturally on the compatible Grassmannian, the group of all invertible operators in H which preserve
the form [ . , . ]. For p between 1 and infinity, in the presence of a fixed [ . , . ]-orthogonal
(direct sum) decomposition of H, H = S_0 + N_0, we study the restricted compatible Grassmannian (an
analogue of the restricted, or Sato Grassmannian). This restricted compatible Grassmannian is shown
to be a submanifold of the Banach space of p-Schatten operators which are symmetric for the form [ .
, . ]. It carries the locally transitive action of the Banach-Lie group of invertible operators
which preserve [ . , . ], and are of the form G = 1 + K, with K in the p-Schatten class. The
connected components of this restricted Grassmannian are characterized by means of of the Fredholm
index of pairs of projections. Finsler metrics which are isometric for the group actions are
introduced for both compatible Grassmannians, and minimality results for curves are proved.
Ore 9:00, Aula Picone
9.00 - 9.40 Hiroshi Matano (University of Tokyo)
Propagating terrace for multi-stable nonlinear diffusion equations
9.45 - 10.25 Mimmo Iannelli (Università di Trento)
A model for describing the structure and growth of epidermis
11.00 - 11.40 Shoshana Kamin (Tel Aviv University)
Prescribed conditions at infinity for parabolic equations
11.45 - 12.25 Roberto Natalini (Istituto per le Applicazioni del Calcolo "M. Picone", CNR)
Hyperbolic perturbations of scalar laws: from oil recovery to vasculogenesis
Ore 9:30
09h30 : Opening: Themes of these days
10h15 : Alain Lecomte: Ludics and modelisation of Socratic dialogues
11h15 : Michele Abrusci: Incompleteness theorems and Transcendental Syntax
12h00 : Mathieu Marion: Dialogue, dialectics, and inferentialism
14h30 : Alberto Naibo: From axioms to computation: A philosophical account of geometry of
interaction
15h15 : Paolo Pistone: Rules, types and the transcendence of second order logic
16h15: Giuseppe Primiero: Resources based interpretation of Ludics
17h00 : General Discussion
Ore 14:30, Aula Picone
14.30 - 15.10 Laurent Veron (Université Francois Rabelais)
Initial trace of positive solutions of weakly superlinear parabolic equations
15.20 - 16.00 Andrea Terracina (Sapienza Università di Roma)
Uniqueness and non-uniqueness results for entropy solutions of forward--backward parabolic
problems
16.10 - 16.50 Michiel Bertsch (Università di Roma "Tor Vergata")
Travelling wave solutions of a system of PDE's
Ore 9:00, Aula Picone
9.00 - 9.40 Wei-Ming Ni (East China Normal University and University of Minnesota)
Competition--diffusion systems
9.45 - 10.25 Lorenzo Giacomelli (Sapienza Università di Roma)
Well-posedness for the Navier-slip thin-film equation in complete wetting
11.00 - 11.40 Henri Berestycki (EHESS)
Propagation in non homogeneous media - the effect of geometry
11.45 - 12.25 Catherine Bandle (University of Basel)
Quasilinear elliptic and parabolic problems with a Hardy potential
Ore 9:30
09h30 : Laurent Keiff: Modalities, Proof theory and Ludics
10h15 : Frederic Nef: Relation and Connection
11h15 : Michele Basaldella: Ludics without designs
12h00 : Arnaud Valence: Towards a Transcendental Euristics
14h30 : Daniele Porello: TBA
15h15 : Pierre Livet: The notion of incompatibility in Brandom's inferentialism
16h15 : Samuel Tronçon: Ludics and Social Interaction
17h00 : General Discussion
Ore 11:30, Aula D'Antoni, Università di Roma II
Seminario di Geometria Algebrica
Presenterò alcuni nuovi risultati sulla fattorialità di threefolds in P^4 aventi solo
singolarità ordinarie (tali cioè che il corrispondente cono tangente è un cono
su una superficie liscia). Enuncerò poi una congettura che generalizza precedenti risultati
ottenuti da Ciliberto-Di Gennaro e Cheltsov nel caso di threefolds nodali. Si tratta di un lavoro in
collaborazione con A. Rapagnetta e P. Sabatino.
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