|09/01/20||Seminario||14:00||15:00||1201 Dal Passo||Gianluca Polenta||ASI Space Science Data Centre||Cosmology through CMB maps|
The Cosmic Microwave Background is a fundamental source of information for cosmology. In the standard inflationary scenario, the CMB can be described to first order as a Gaussian random field on the sphere, and as such cosmological information is encoded in the two-point correlation function or in the angular power spectrum. To derive these quantities as well as the likelihood function needed to estimate the cosmological parameters, a number of estimators have been developed following different trade-off between optimality, unbiasedness, and computational resources, also depending on the characteristics of the dataset to be analysed. In this talk I will review the different classes of estimators used in the CMB data analysis, focusing in particular to the solutions adopted for the ESA Planck satellite, which produced CMB full sky maps of unprecedented quality. Finally, I will briefly discuss how CMB non-Gaussianity, isotropy, and those anomalies found in the analysis of Planck data can be used to further test the inflationary paradigm.
This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.
|08/01/20||Seminario||16:00||17:00||1201 Dal Passo||Michael Mueger||Radboud University||On a conjecture of Olivier Mathieu
I will explain a conjecture due to Olivier Mathieu (ca. 1995) concerning
harmonic analysis on compact connected Lie groups, some of its
applications and earlier results. Then I will talk about recent work on
aspects of the conjecture, joint with Lars Tuset (Oslo), which will
appear in 3 papers. (The first is arXiv:1910.12148, to appear in Indag.
|19/12/19||Seminario||14:00||15:00||1201 Dal Passo||Peyman Eslami||Inducing schemes for piecewise expanding maps of R^n
For piecewise expanding maps of R^N I will show how to construct an inducing scheme where the base map is Gibbs-Markov and the return times have exponential tails. Inducing schemes such as this can then be used to prove various statistical properties for dynamical systems with some hyperbolicity.
|18/12/19||Seminario||14:00||15:00||1201 Dal Passo||Gianluca Marzo||Tor Vergata||Fully functorial resolutions of complex analytic singularities|
Phd thesis defence
|17/12/19||Seminario||14:30||15:30||1201 Dal Passo||Leonard Kreutz||University of Münster||From Crystals to Polycrystals |
In this talk we discuss the emergence of an energy defined on rigid polycrystalline materials from atomistic systems with the Heitmann-Radin Sticky disc energy. The discrete energy is a suitably rescaled pair interaction energy, where the interaction potential models the atoms as hard spheres, that is minimized, when two spheres are tangential. Furthermore, the discrete energy is frame invariant and no underlying reference frame on the atomistic configurations is assumed. The continuum parameter is a piecewise-constant function that describes the local orientation and micro-translation of the configuration. The limit energy, derived by means of Gamma-convergence, is local and concentrated on the grain boundaries, i.e. on the boundaries of the zones where the underlying microscopic configuration has constant orientation. The surface energy density depends on the relative orientation of the two grains, their microscopic translation misfit, and the normal to the interface. We point out the differences of the derived continuum energy density with respect to the Read-Shockley formula. This is joint work with Manuel Friedrich and Bernd Schmidt.
|16/12/19||Seminario||16:20||17:20||1200 Biblioteca Storica||Kieran O'Grady||Sapienza Università di Roma||Fasci modulari su varieta' hyperkaehler
Un fascio privo di torsione su una varieta' hyperkaehler X e' modulare
se il suo discriminante (una classe caratteristica di grado 4) soddisfa una certa condizione
che, per esempio, e' soddisfatta se il discriminante e' un multiplo di c_2(X). Per i fasci modulari la variazione della stabilita' come funzione della polarizzazione e' analoga a quella nel caso di fasci su superfici. Questo ci permette di dimostrare risultati di
esistenza e unicita' a meno di isomorfismo per fibrati vettoriali stabili con certi caratteri di Chern. Una conseguenza e' la birazionalita' dell'applicazione dei periodi dello spazio dei moduli di varieta' di Debarre-Voisin.
|16/12/19||Seminario||15:10||16:10||1200 Biblioteca Storica||Lie Fu ||Université Claude Bernard Lyon 1||On the motive of some hyper-Kaehler varieties of O'Grady-10 type.
The general question is to investigate how the motive of a hyper-Kähler variety can be obtained by tensor operations from a surface-like (weight-2) motive. I will present two ways to make this precise, mainly focus in the case of O'Grady-10 type varieties.
First, we show that the Chow motive of O'Grady-10-type crepant resolutions of moduli space of semistable sheaves on a K3 surface is in the tensor subcategory generated by the Chow motive of the surface. As consequences, we show the standard conjecture for those
resolutions and we obtain results on the Voevodsky motive of the (open) moduli space of stable locus and the original singular moduli space. Second, we show that the André motive of any hyper-Kähler variety of O'Grady-10 deformation type lies in the tensor
subcategory generated by its degree-2 part. As a consequence, their motive is of abelian type and the Mumford-Tate conjecture holds for them. This is a joint work with Salvatore Floccari and Ziyu Zhang.
|16/12/19||Seminario||14:00||15:00||1200 Biblioteca Storica||Valeria Bertini||Tor Vergata e Strasbourg||Rational curves on irreducible symplectic varieties of OG10 type|
Phd thesis defence
|13/12/19||Seminario||15:30||16:30||1101 D'Antoni||Pietro Sabatino ||Liceo Mamiani||On a generalization of the Bogomolov-Miyaoka-Yau inequality and an explicit
bound for the log-canonical degree of curves on open surfaces
Let X, D be respectively a smooth projective surface and a simple normal
crossing divisor on X. Suppose ?(X,K_X+D) ? 0, given an irreducible curve C
on X and a rational number ? ? [0,1], following ideas introduced by Miyaoka,
we define an orbibundle E_? as a subsheaf of log differentials on a suitable
Galois cover of X and prove a Bogomolov-Miyaoka-Yau inequality for this
bundle. We briefly compare this construction to similar ones of e.g. Megyesi
and Langer. As a consequence of this Bogovomolov-Miyaoka-Yau inequality we
deduce, in the case K_X+D big and nef and (K_X+D)^2 > chi(X D), a bound
(K_X+D)cdot C by an explicit function of the invariants (K_X+D)^2, the
topological Euler-Poncaré characteristic of the open surface chi(X D) and
chi( ilde C? D), the topological Euler-Poncare' characteristic of the
normalization of C minus the points mapping on D.
|13/12/19||Seminario||14:30||15:30||1101 D'Antoni||Alexander PÜTZ||Università di Roma "Tor Vergata"||Linear degenerations of affine Grassmannians and moment graphs
Every projective variety is a quiver Grassmannian. Hence, we can use representation theory of quivers to study the geometry of certain projective varieties. In this talk we apply it to study the affine Grassmannian. Namely we identify certain finite approximations of it with quiver Grassmannians for the loop quiver. In this way we can study the geometry of the affine Grass-mannian via the limit of the approximations. We also examine how the geometry changes with linear degenerations and find out that it behaves very different from the non-affine setting. There is an action of a one-dimensional torus on the affine Grassmannian and its linear degenerations which induces a cellular decomposition. Based on the combinatorics of this decomposition we can compute Euler characteristics, Poincaré polynomials and cohomology. In the non-degenerate setting, we rediscover some results obtained with the combinatorics of the affine Weyl group.