Pagina 5

Date | Type | Start | End | Room | Speaker | From | Title |
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26/11/19 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Chong-Qing Cheng | Nanjing University | A new way to cross double resonance In the study of Arnold diffusion, especially after the diffusion in a-priori unstable case has been solved, the main difficulty is to cross double resonance, as foreseen by Arnold in the last 1960's. In this talk we shall describe a new way to cross double resonance, which makes it rather simple to prove Arnold diffusion in nearly integrable Hamiltonian systems with three degrees of freedom. |

22/11/19 | Seminario | 15:45 | 16:45 | 1101 D'Antoni | Guido Lido | Tor Vergata e Leiden | The Poincaré torsor and the quadratic Chabauty method. Let C be a curve of genus g>1 defined over the rationals and let J be its Jacobian. Faltings's theorem states that C has only finitely many rational points, but in practice there is no general procedure to provably compute the set C(Q). When the rank of J(Q) is smaller than g, we can use Chabauty's method: embedding C in J the set C(Q) is a subset of the intersection of C(Qp) and the closure of J(Q) inside the p-adic manifold J(Qp); since this intersection is finite and computable up to finite precision we can use it to compute C(Q). Minhyong Kim has generalized this method inspecting the (Qp-prounipotent etale) fundamental group of C and his ideas have been made effective in some new cases by Balakrishnan, Dogra, Muller, Tuitman and Vonk: their "quadratic Chabauty method" works when the rank of
J(Q) is smaller than g+s-1 (with s the rank of the Neron-Severi group of J). In this seminar we describe a reinterpretation of the quadratic Chabauty method that does not need the fundamental group of C but uses only some geometry over the integers and the Gm-torsor associated to the Poincaré bundle over J. This work is in collaboration and under the supervision of Bas Exidhoven. |

22/11/19 | Seminario | 14:30 | 15:30 | 1101 D'Antoni | Some older and some recent results on the ind-varieties G/P for the ind-groups G = GL(∞) , O(∞) , Sp(∞) About 15 years ago, Dimitrov and I worked out the flag realizations of the homogeneous ind-varieties GL(∞)/P for arbitrary splitting parabolic ind-subgroups P. An essential difference from the finite-dimensional case is that we have to work with generalized flags, not with usual flags. Generalized flags are chains of subspaces which have more interesting linear orders. In the first part of the talk, I will recall our results with Dimitrov. In the second part, I will explain(without proof) two recent results. The first one (joint with A. Tikhomirov) is a purely algebraic-geometric construction of the ind-varieties of generalized flags. The second one (joint with L.Fresse) answers the following question: on which multiple ind-varieties of generalized flags, i.e. direct products of ind-varieties of generalized flags, does GL(∞) act with finitely many orbits? N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006 | ||

19/11/19 | Seminario | 16:00 | 17:00 | 1101 D'Antoni | Yuri Kozitski | Lublin | Stochastic evolution of an interacting particle system in the
continuum: an analytic approach. An infinite system of point particles placed in the continuum is
studied. Its constituents perform random jumps with mutual repulsion, and
this evolution is described by constructing path measures of certain kind
on the space of possible trajectories of the system. |

15/11/19 | Seminario | 09:30 | 12:30 | 1201 Dal Passo | Giovanni Peccati | University of Luxembourg | MINI-CORSO: The Malliavin-Stein Method I will provide a self-contained introduction to a collection
of probabilistic techniques developed in the last decade, focussing on
quantitative limit theorems for non-linear functionals of Gaussian
fields, obtained by combining two techniques: (i) the Malliavin calculus
of variations, and (ii) Stein's method for probabilistic approximations.
I will develop in full detail at least one geometric application related
to the structure of level sets of Gaussian fields, and I will try to
point out a number of further directions of research, connected e.g. to
concentration estimates, entropic bounds, discrete geometric structures
and the analysis of Boolean functions. |

14/11/19 | Seminario | 14:00 | 17:00 | 1201 Dal Passo | Giovanni Peccati | University of Luxembourg | MINI-CORSO: The Malliavin-Stein Method I will provide a self-contained introduction to a collection
of probabilistic techniques developed in the last decade, focussing on
quantitative limit theorems for non-linear functionals of Gaussian
fields, obtained by combining two techniques: (i) the Malliavin calculus
of variations, and (ii) Stein's method for probabilistic approximations.
I will develop in full detail at least one geometric application related
to the structure of level sets of Gaussian fields, and I will try to
point out a number of further directions of research, connected e.g. to
concentration estimates, entropic bounds, discrete geometric structures
and the analysis of Boolean functions. |

13/11/19 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Robin Hillier | Lancaster University | Roots of completely positive maps We introduce the concept of completely positive roots of completely positive maps on operator algebras. We do this in different forms: as asymptotic roots, proper discrete roots and as continuous one-parameter semigroups of roots. We present structural and general existence and non-existence results, some special examples in settings where we understand the situation better, and several challenging open problems. Our study is closely related to Elfving's embedding problem in classical probability and the divisibility problem of quantum channels. |

13/11/19 | Seminario | 15:00 | 16:00 | 1200 Biblioteca Storica | Ernesto Mistretta | Università di Padova | Holomorphic symmetric differentials, abelian variesties, complex tori, and parallelizable compact complex manifods
We review some recent constructions obtained with S. Urbinati on positivity, base loci, and Iitaka fibrations for higher rank vector bundles, then use some of these to obtain a biholomorphic and a bimeromorphic characterization of abelian varieties.
Then we see how to extend some of these results to complex tori and to compact complex parallelizable manifolds. |

12/11/19 | Seminario | 16:00 | 17:00 | 1101 D'Antoni | David Marti'-Pete | Polish Academy of Science | On the connectivity of the escaping set in the punctured plane A function $f$ is a transcendental self-map of the punctured plane if $f:mathbb{C}^* omathbb{C}^*$ is a holomorphic function,
$mathbb{C}^*=mathbb{C}setminus{0}$, and both $0$ and $infty$ are essential singularities of $f$. For such maps, the escaping set $I(f)$ consists of the points whose orbit accumulates to a subset of ${0,infty}$.
We will look at the connectivity of $I(f)$ and show that either $I(f)$ is connected, or has infinitely many components.
We also proved that $I(f)cup {0,infty}$ is either connected, or has exactly two components,
one containing $0$ and the other $infty$. This gives a trichotomy regarding the connectivity of the sets $I(f)$ and
$I(f)cup {0,infty}$, and we will give examples of functions for which each case arises.
To give an example of a transcendental self-map $f$ of $C^*$ for which $I(f)$ is connected, we adapted the so-called
spider's web structure due to Rippon and Stallard to the punctured plane. Finally, whereas Baker domains of transcendental entire
functions are simply connected, we showed that Baker domains can be doubly connected in $C^*$ by constructing the first such example. We also proved that if $f$ has a doubly connected Baker domain, then its closure contains both $0$ and $infty$, and hence
$I(f)cup{0,infty}$ is connected in this case. This is a joint work with Vasiliki Evdoridou (Open University) and Dave Sixsmith (University of Liverpool). |

12/11/19 | Seminario | 14:45 | 15:45 | 1201 Dal Passo | Gabriele Mondello | Sapienza, Università di Roma | Minimizing immersions of a hyperbolic surface in a hyperbolic 3-manifold Let (S,h) be a closed hyperbolic surface and M be a hyperbolic 3-manifold. We consider incompressible maps from S to M that are critical points of an energy functional F which is homogeneous of degree 1. We prove the uniqueness of smooth minimizing maps from (S,h) to M in a given homotopy class. When (S,h) is fixed, smooth minimizing maps from (S,h) are described by a simple holomorphic datum on S: a complex self-adjoint Codazzi tensor of determinant 1. The space of admissible data is smooth and naturally equipped with a complex structure, for which the monodromy map taking a data to the monodromy representation of the image is holomorphic. Minimizing maps are in this way reminiscent of shear-bend coordinates, with the complexification of F analoguous to the complex length. This is joint work with Francesco Bonsante and Jean-Marc Schlenker. |