Pagina 7

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

12/03/19 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Alessandra Lunardi | Universita' di Parma | Sobolev and BV functions in infinite dimension.
In Hilbert or Banach spaces $X$ endowed with a good probability measure $mu$ there are a few "natural"
definitions of Sobolev spaces and of spaces of bounded variation functions. The available theory deals
mainly with Gaussian measures and Sobolev and BV functions defined in the
whole $X$, while the study and Sobolev and BV spaces in domains, and/or with respect to non Gaussian
measures, is largely to be developed.
As in finite dimension, Sobolev and BV functions are tools for the study of different problems, in particular
for PDEs with infinitely many variables, arising in mathematical physics in the modeling of systems with an
infinite number of degrees of freedom, and in stochastic PDEs through Kolmogorov equations.
In this talk I will describe some of the main features and open problems concerning such function spaces. |

11/03/19 | Colloquium | 14:30 | 15:30 | 1201 Dal Passo | Kazhdan-Lusztig Theory The study of continous actions of groups like GL( n;R) and GL(n;C) on Banach spaces leads to interesting algebraic questions. This field has seen great progress recently, and I want to talk on it. N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006 | ||

04/03/19 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Wonderful models for generalized Dowling lattices Given a subspace arrangement, De Concini and Procesi in the '90s described the construction of a variety associated to it, namely its wonderful model. An important feature of these model is that some of its geometric aspects are linked to some combinatorical properties of the subspace arrangement, in particular the description of its boundary and its Betti numbers. During the talk I will consider the subspace arrangement associated to a generalized Dowling lattice, a combinatorial object introduced by Hanlon. The aim is to study the wonderful model associated to it and to give a description of its boundary. To deal with this I will use a bijection between the set of boundary components of the wonderful model and a family of graphs. This is a joint work with Giovanni Gaiffi. | ||

27/02/19 | Colloquium | 14:30 | 15:30 | 1201 Dal Passo | On short closed geodesics, shadows of balls and polar bodies How long is the shortest closed geodesic on a Riemannian sphere? How large is the shadow of a symplectic ball? How large is the volume of the polar of a centrally symmetric convex body? I will discuss how these seemingly different problems can be addressed within the setting of Reeb dynamics. N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006 | ||

26/02/19 | Seminario | 16:00 | 17:00 | 1101 D'Antoni | Samuele Mongodi | Politecnico di Milano | Holomorphicity of slice-regular functions Abstract: In 2010, Ghiloni and Perotti showed how a slice-regular function
f from a real alternative algebra A to itself is induced, in a suitable
sense, by a holomorphic function F from the complex numbers to the
complexification of A; however, there is no evident "holomorphic" link
between the values of f and the values of F.
I want to show, in the particular case where A is the algebra of
quaternions H, how the set of values of F which induce a zero of f is
actually a complex subspace of the complexification of H and how a number
of properties of slice-regular functions can be therefore deduced from the
classical properties of holomorphic functions.
Moreover, this approach gives an identification of the set of imaginary
units of H with a complex submanifold of a (complex) grassmannian, or, in
other words, how we obtain a natural complex structure on such set which is
compatible with slice-regularity; this point of view is linked to the work
of Gentili, Salamon, Stoppato on the twistorial lift of a slice-regular
function.
If time permits, I'll hint also to the general approach for the case of an
associative algebra. |

26/02/19 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Claudio Bonanno | Universita' di Pisa | Asymptotic behaviour of chains of interacting particles One interesting problem in the study of chains of particles with nonlinear interactions is to describe and classify the possible asymptotic behaviours. The possible behaviours obviously depends on the nature of the interactions, but there are similarities in large classes of systems. Considering Hamiltonian systems I will discuss the role played by the existence of a conservation law independent from energy, and introduce a characterization of the asymptotic behaviours based on a notion of complexity. |

25/02/19 | Seminario | 14:30 | 15:30 | 1101 D'Antoni | Recent developments on degenerations of flag and Schubert varieties I'll recall flag varieties and Schubert varieties, and building on that PBW and linear degenerations. This first part is meant to be an introduction for Master and Phd-students. I'll proceed with recent results on PBW degenerations of Schubert vareties, explaining triangular and rectangular Weyl group elements. The talk will end with several open questions, discussing the current limit of generalizations. N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006 | ||

21/02/19 | Seminario | 16:00 | 17:00 | 1101 D'Antoni | Marco Abate | Universita' di Pisa | Carleson measures and Toeplitz operators on weighted Bergman spaces Carleson measures were introduced by Carleson in his celebrated solution of the corona
problem; since then they have become an interesting subject of study
on their own, mainly because they can be characterised in many different ways, both analytic
and geometrical. In this talk we shall apply Carleson measures to the study of mapping
properties of Toeplitz operators between weighted Bergman spaces on strongly pseudo convex
domains. More precisely, if $T^eta_mu$ is the Toeplitz operator associated to the measure
$mu$ and having as kernel the Bergman kernel of the weighted Bergman space $A^2_eta$, then
(if $eta$ is large enough) $T^eta_mu$ maps $A^{p_1}_{alpha_1}$
into $A^{p_2}_{alpha_2}$ if and only if $mu$ is a Carleson measure of a suitable exponent.
(Joint work with S. Mongodi and J. Raissy). |

21/02/19 | Seminario | 15:00 | 16:00 | 1201 Dal Passo | Gilberto Bini | Università di Milano Statale | "A meaningful invariant in birational geometry" [Algebraic Geometry Seminar - in the framework of
the Research Project "Families of curves: their moduli and their related varieties" - Mission Sustainability
Tor Vergata, CUP: E81|18000100005, Principal Investigator: F. Flamini]
In this talk we will survey on the state of the art of some relevant conjectures for the birational classification of complex projective varieties with respect to an invariant that has not been completely utilised but seems to be potentially meaningful: the pseudo-effective dimension.
Link: http://www.mat.uniroma2.it/~flamini/seminari/annuncio.html
[Algebraic Geometry Seminar - in the framework of the Research Project "Families of curves: their moduli and their related varieties" - Mission Sustainability
Tor Vergata, CUP: E81|18000100005, Principal Investigator: F. Flamini] |

20/02/19 | Seminario | 14:00 | 17:00 | 1101 D'Antoni | Espen SANDE | University of OSLO | An introduction to Kolmogorov n-widths |