Pagina 2

Date | Type | Start | End | Room | Speaker | From | Title |
---|---|---|---|---|---|---|---|

10/06/19 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Towards degenerations for algebras with self-dualities A parabolic subgroup P of a classical Lie group G acts on the nilpotent cone N of nil-potent complex matrices in Lie(G) via conjugation. If N is restricted to the subvariety of 2-nilpotent matrices, then the number of orbits is finite and we can describe a parametrization of the orbits by using a translation to the symmetric representation theory of a finite-dimensional algebra with self-duality. Our main goal is the description of the orbit closures and we discuss first results. These results are obtained via degenerations of symmmetric representations of a certain algebra with self-duality, and we show which of them hold in general. This is based on work in progress with G. Cerulli Irelli and F. Esposito. | ||

07/06/19 | Seminario | 16:30 | 18:00 | 1101 D'Antoni | Vlad Bally | Université Paris-Est | Convergence in Distribution Norms in the CLT and Application to Trigonometric Polynomials
Under some regularity condition on the random variables at hand, we prove convergence in distribution norms in the CLT and we also derive some local developments (Edgeworth expansions). We use these results in order to study the asymptotic behavior of the number of roots of trigonometric polynomials with random coefficients. |

03/06/19 | Seminario | 12:00 | 13:00 | 1201 Dal Passo | Quantum principal bundles over projective bases In non commutative geometry, a quantum principal bundle over an affine base is recovered through a deformation of the algebra of its global sections: the property of being a principal bundle is encoded by the notion of Hopf Galois extension, while the local triviality is expressed by the cleft property. The quantum algebra of the base space is realized as suitable coinvariants inside the global sections of the quantum principal bundle. We want to examine the case of a projective base X in the special case X=G/P , where G is a complex semisimple group and P a parabolic subgroup. We will substitute the coordinate ring of X with the homogeneous coordinate ring of X with respect to a projective embedding, corresponding to a line bundle L obtained via a character of P. The quantization of the line bundle will come through the notion of quantum section and the quantizations of the base (a quantum flag) will be obtained as semi-coinvariants. The quantization of G will then be interpreted as the quantum principal bundle on the quantum base space X, obtained via a quantum section. (joint work with P. Aschieri and E. Latini) | ||

31/05/19 | Colloquium | 15:30 | 16:20 | 1101 D'Antoni | Alessandra Sarti | Univ. Poitiers (France) | Colloquium in Algebraic Geometry: K3 surfaces and their group of symmetries
Particularly interesting objects in algebraic geometry are K3 surfaces, which are special complex algebraic surfaces. The most easy example of such a surface is the zero set of a homogeneous polynomial of degree four in the three dimensional complex projective space. The name was given by André Weil in 1958 in honour of three famous mathematicians: Kummer, Kähler and Kodaira and in honour of the K2 mountain at Cachemire. Their symmetry group is an important tool to understand their geometry. I will first show some remarkable properties of K3 surfaces and in particular the important role of lattice theory, then I will show some classic and recent results on their symmetry groups.
[Department Colloquium (General audience), in the framework of MIUR Excellence Project Math@Tov, CUP E83C18000100006] |

31/05/19 | Colloquium | 14:30 | 15:20 | 1101 D'Antoni | Samuel Boissiere | Univ. Poitiers (France) | Colloquium in Algebraic Geometry:
Involutions on the Hilbert square of a K3 surface
I will use K3 surfaces with special geometry to construct involutions on the Hilbert square of a K3 surface. The existence of such involutions can be proven using the Torelli theorem for hyper-Kaehler manifolds, but it is a challenging problem to produce concrete realizations.
[Department Colloquium (General audience), in the framework of MIUR Excellence Project Math@Tov, CUP E83C18000100006] |

30/05/19 | Seminario | 15:30 | 16:20 | 1200 Biblioteca Storica | Samuel Boissiere | Univ. Poitiers (France) | Some families of projective varieties uniformized by the 10-dimensional complex ball
In a famous paper, Allock, Carlson and Toledo described the moduli space of cubic threefolds as the arithmetic quotient of the complementary of a hyperplane arrangement in the 10-dimensional complex ball. I will present an interpretation of this moduli space as the one parametrizing a family of order three nonsymplectic automorphisms on hyperkaehler manifolds deformation equivalent to the Hilbert square of a K3 surface. This is a collaboration with Chiara Camere and Alessandra Sarti.
[Algebraic Geometry Seminar, in the framework of MIUR Excellence Project Math@Tov, CUP E83C18000100006] |

30/05/19 | Seminario | 14:30 | 15:20 | 1200 Biblioteca Storica | Alessandra Sarti | Univ. Poitiers (France) | On non-symplectic automorphisms of K3 surfaces
Automorphisms of K3 surfaces were very much studied in the last years. Depending on the action on the holomorphic two form which can be trivial or not, they are called symplectic or non-symplectic. The aim of the talk is to present recent results in the study of non--symplectic automorphisms of 2-power order. In particular in the case of the order 16 I completely describe the families of K3 surfaces carrying such automorphisms.
[Algebraic Geometry Seminar, in the framework of MIUR Excellence Project Math@Tov, CUP E83C18000100006] |

29/05/19 | Colloquium | 16:00 | 17:00 | 1201 Dal Passo | Albert Fathi | Georgia Institute of Technology (USA) | Singularities of solutions of the Hamilton-Jacobi equation. A toy model: distance to a closed subset
This is a joint work with Piermarco Cannarsa and Wei Cheng.
The distance function $d_F$ to a closed subset $F$ of Euclidean space ${f R}^k$ is given by
$$d_F(x)=inf_{fin F}|x-f|.$$
It is a Lipschitz, hence differentiable almost everywhere. We will discuss some topological properties of the set ${
m Sing}(d_F)$ of points where $d_F$ is not differentiable.
More generally, we will discuss properties of the set of singularities of a viscosity solution of the Hamilton-Jacobi equation
$$partial_tU+H(x,partial_xU)=0,$$
when $H$ is a Tonelli Hamiltonian.
We will give applications in Riemannian geometry.
We will explain during the lecture all notions (beyond common knowledge) necessary to understand it. |

27/05/19 | Seminario | 14:00 | 15:00 | 1201 Dal Passo | The integral form of the universal enveloping algebra of twisted affine sl_{3} In the representation theory of a semisimple Lie algebra L, the subring of the universal enveloping algebra U(L) generated by suitable divided powers arises naturally, thus leading to construct an integral form of U(L). Kostant and Cartier indipendently defined this form and explicitly constructed integral bases when L is finite. Their construction has later been generalized to the untwisted affine case by Garland. An analogous work by Fisher-Vasta extends the construction of the integral form of U(L) to the affine twisted Kac-Moody algebra of rank 1 (type A^{2}_{2}). These works are based on complicated commutation formulas, whose regularity remains hidden; moreover, in the twisted case there are some problems both with the statement and the proof. The aim of this talk is to give a correct description of the integral form of the enveloping algebra of type A^{2}_{2} , providing explicit and compact commutation relations, so to reach a deeper comprehension and drastic simplification of the problem. This is achieved by means of a careful use of the generating series of families of elements and of the properties of the ring of symmetric functions. | ||

23/05/19 | Seminario | 16:00 | 17:30 | 1101 D'Antoni | Alessia Caponera | Sapienza Università di Roma | Asymptotics for spherical autoregressions We present a class of space-time processes, which can be viewed as functional autoregressions taking values in the space of square integrable functions on the sphere. We exploit some natural isotropy requirements to obtain a neat expression for the autoregressive functionals, which are then estimated by a form of frequency-domain least squares. For our estimators, we are able to show consistency and limiting distributions. We prove indeed a quantitative version of the central limit theorem, thus deriving explicit bounds (in Wasserstein metric) for the rate of convergence to the limiting Gaussian distribution; to this aim we exploit the rich machinery of Stein-Malliavin methods. Our results are then illustrated by numerical simulations. |