Notiziario Scientifico

Notiziario dei seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma

Settimana dal 9 al 15 gennaio 2017


Lunedì 9 gennaio 2017
Ore 14:30, aula di Consiglio
seminario di Analisi Matematica
Dorin Bucur (Université de Savoie)
Best constant in Sobolev inequalities with trace terms


Lunedì 9 gennaio 2017
Ore 15:00, Biblioteca - Sala Ingegneria Geotecnica, dipartimento di Ingegneria Strutturale e Geotecnica, via Eudossiana 18, Roma
seminario
Matteo Pezzulla (Boston University)
Geometry and Instabilities in Growing Shells


Martedì 10 gennaio 2017
Ore 14:00, aula di Consiglio
seminario di Probabilità e Statistica Matematica
Antonio Lijoi (Università di Pavia)
Bayesian nonparametric inference with heterogeneous data
The talk provides an overview of some recent work on random probability measure vectors and their role in Bayesian statistics. Indeed, dependent nonparametric priors are useful tools for drawing inferences on data that arise from different, though related, studies or experiments and for which the usual exchangeability assumption is not satisfied. The presentation will focus on models based on completely random measures, or suitable transformations thereof, that have an additive, a hierarchical and a nested structure. Some of their distributional properties relevant for prediction will be discussed. These theoretical results are, then, used for devising Markov chain Monte Carlo algorithms that will be implemented within some illustrative examples for analyzing data in the contexts of species sampling problems and survival analysis.


Martedì 10 gennaio 2017
Ore 14:30, aula 1B1 (pal. RM002), dipartimento di Scienze di Base e Applicate per l'Ingegneria, via A. Scarpa 14
seminario di Geometria
Maria Gordina (University of Connecticut)
Stochastic analysis and geometric functional inequalities
We start by recalling that on a Euclidean space there is a connection between the spectrum of the Laplacian and the speed of heat diffusion, which leads to several functional inequalities, such as Poincare, Nash etc. Moving to a curved space, we see that the geometry of the underlying space plays an important role in such an analysis. If, in addition, the state space is infinite-dimensional, the log-Sobolev inequality becomes a useful fact which can be applied to describe entropic convergence of the heat flow to an equilibrium. A probabilistic point of view comes from a path integral representation of the heat flow for stochastic differential equations driven by a Brownian motion. In particular, we will discuss how the Cameron-Martin-Girsanov type theorem is related to certain functional inequalities. The talk will review recent advances in the field, including elliptic and hypo-elliptic settings over both finite- and infinite-dimensional spaces.


Martedì 10 gennaio 2017
Ore 15:00, aula B, Università di Roma Tre, via della Vasca Navale 84
colloqui di Fisica
Massimiliano Lattanzi (Università di Ferrara e INFN)
Constraining neutrino physics through observations of the cosmic microwave background
Cosmological observations represent a powerful tool to constrain neutrino physics, complementary to laboratory experiments. In particular, observations of the cosmic microwave background (CMB) have the potential to constrain the properties of relic neutrinos, as well as of additional light relic particles in the Universe. The data released by the Planck collaboration in 2015 provide the most precise publicly available measurements to date of the temperature and polarization anisotropies of the cosmic microwave background. I will present current constraints on neutrino properties, including their mass and effective number, from the most recent Planck data, possibly in combination with other cosmological probes, especially galaxy surveys. I will also discuss prospects from future experiments, both from the ground and from space.


Mercoledì 11 gennaio 2017
Ore 14:00, aula di Consiglio
seminario di Algebra e Geometria
Sergio Ciamprone (Sapienza Università di Roma)
Certain braided weak Hopf C*-algebras associated to modular categories
The talk is a presentation my Ph.D. thesis. Semisimple quotient categories arising from the representation theory of Drinfeld-Jimbo quantum groups at roots of unity play a crucial role in many areas of physics and mathematics. In this talk we will show how one can construct in the type A case and for certain roots of unity a family of quantum groupoids whose representation theory is equivalent to these categories. The construction was originally inspired by some work for sl2 of the early 90s in the physics literature and makes use of a Hilbert space construction associated to the quotient category due to Wenzl in the late 90s. These groupoids are weak Hopf C*-algebras, in a sense which is new in the literature. In light of these facts, a generalization of the Haring-Oldenburg's reconstruction theorem will be given. Finally, the quantum groupoids introduced above will be presented by generators and relations in some special cases. Most of the talk is based on a joint work with C. Pinzari.


Mercoledì 11 gennaio 2017
Ore 14:30, aula Dal Passo, Università di Roma Tor Vergata
colloquium di Dipartimento
Renato Calleja (IIMAS-UNAM, Mexico)
Quasi-periodic solutions in conformally symplectic systems
Many problems in Celestial Mechanics are described by conformally symplectic systems (e.g. mechanical systems with a friction proportional to the velocity). The symplectic structure provides geometric identities that are used to prove theorems of existence of quasi-periodic solutions that are in an 'a-posteriori' format. The a-posteriori approach presents several advantages over the classical perturbation methods and provides results on regularity, convergence of Lindstedt series and efficient algorithms to approximate the quasi-periodic solutions numerically. I will discuss other implications of this approach including a criterion for the breakdown of analyticity and hyperbolicity [C-Figueras-12], local behaviour near invariant tori, and shape and numerical approximation of domains of analyticity of invariant tori as the friction vanishes to zero [Bustamante-C-17]. This is a joint work with Alessandra Celletti, Rafael de la Llave.


Mercoledì 11 gennaio 2017
Ore 15:00, aula di Consiglio
seminario di Algebra e Geometria
Bruno Klingler (Jussieu)
Chern's conjecture for special affine manifolds
An affine manifold X (in the sense of differential geometry) is a differentiable manifold admitting an atlas of charts with value in an affine space with locally constant affine change of coordinates. Equivalently, it is a manifold admitting a flat torsion free connection on its tangent bundle. Around 1955 Chern asked if there is any topological obstruction to the existence of an affine structure on a compact manifold X. He conjectured that the Euler characteristic e(TX) of any compact affine manifold has to vanish. I will discuss this conjecture and a proof when X is special affine (i.e. X is affine and moreover admits a parallel volume form). Surprisingly (or not), the proof relies on algebraic methods coming from hypercomplex geometry.


Venerdì 13 gennaio 2017
Ore 12:00, aula B
discussione tesi di Dottorato
Andrea Aspri (Sapienza Università di Roma)
Analysis of a linear elastic model relative to a small pressurized cavity embedded in the half-space


Venerdì 13 gennaio 2017
Ore 16:00, aula Picone
seminario per insegnanti (Piano Lauree Scientifiche)
Stefano Finzi Vita (Sapienza Università di Roma), Elena Savinelli (Liceo De Sanctis, Roma) e Luca Sbano (Liceo Colonna, Roma)
Algoritmo. Alcuni spunti per un'attività di laboratorio al Liceo Matematico



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