Pagina 3

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

04/12/18 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Benedetta Pellacci | Universita' della Campania | Asymptotic spherical shapes in some spectral optimization problems
We study the positive principal eigenvalue of a weighted problem associated with the Neumann Laplacian. This analysis is related to the investigation of the survival threshold in population dynamics. When trying to minimize such eigenvalue with respect to the weight, one is lead to consider a shape optimization problem, which is known to admit spherical optimal shapes only in very specific cases. We investigate whether spherical shapes can be recovered in general situations, in some singular perturbation limit. We also consider a related problem, where the diffusion is triggered by a fractional
$s$-Laplacian, and the optimization is performed with respect to the fractional order $sin(0,1]$. These are joint works with Dario Mazzoleni and Gianmaria Verzini. |

03/12/18 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Comparing commutative and noncommutative resolutions of singularities Quotient singularities for reductive groups admit the canonical Kirwan (partial) resolution of singularities, and often also a noncommutative resolution. We will motivate the occurrence of noncommutative resolutions and compare them to their commutative counterparts (via derived categories in terms of the Bondal-Orlov conjecture). This is a joint work with Michel Van den Bergh. | ||

20/11/18 | Colloquium | 14:30 | 16:30 | 1201 Dal Passo | Masayasu Mimura | Musashino University/Meiji University | Transient Self-Organization: Closed Systems vs. Open systems of Reaction and Diffusion After Turing?s theoretical prediction on biological pattern formation, various types of patterns related to self-organization can be discovered in open systems due to the interaction of reaction with
diffusion. Turing said in his paper ?The model will be a simplification and an idealization, and consequently a falsification. It is to be hoped that the features retained for discussion are those of
greatest importance in the present state of knowledge?. Nevertheless, mathematical communities have been much influenced by his theory. We already recognize that open systems of reaction and diffusion have
generated enormous rich behaviors. On the other hand, closed systems have been gradually less interesting. However, I would like to emphasize that new biological pattern formation can be observed even in
closed systems as the consequence of transient self-organization, and that the theoretical understanding of such patterns is a very important subject in nonlinear mathematics. |

16/11/18 | Seminario | 17:15 | 18:15 | 1201 Dal Passo | Standard Monomial Theory via Newton-Okounkov Theory Sequences of Schubert varieties, contained in each other and successively of codimension one, naturally lead to valuations on the field of rational functions of the flag variety. By taking the minimum over all these valuations, one gets a quasi valuation which leads to a flat semi-toric degeneration of the flag variety. This semi-toric degeneration is strongly related to the Standard Monomial Theory on flag varieties as originally initiated by Seshadri, Lakshmibai and Musili. This is work in progress jointly with Rocco Chirivi and Xin Fang. | ||

16/11/18 | Seminario | 15:45 | 16:45 | 1201 Dal Passo | Quiver Grassmannians, Q-intersection and Horn conditions The abstract is available here. | ||

16/11/18 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Automorphisms of almost homogeneous varieties The automorphism group of a projective variety X is known to be a “locally algebraic group”, extension of a discrete group (the group of components) by a connected algebraic group. But the group of components of Aut(X) is quite mysterious; in particular, it is not necessarily finitely generated. In this talk, we will discuss the structure of Aut(X) when X has an action of an algebraic group with an open dense orbit.
In particular, we will see that the group of components is arithmetic (and hence finitely generated) under this assumption. | ||

06/11/18 | Seminario | 16:00 | 17:00 | 1101 D'Antoni | Tatsuo Suwa | Hokkaido University | Relative Dolbeault cohomology and its application to the Sato hyperfunction
theory
The Cech-de Rham cohomology together with its integration theory has been
effectively used in various problems related to localization of
characteristic classes. Likewise we may develop the Cech-Dolbeault
cohomology theory and on the way we naturally come up with the relative
Dolbeault cohomology.
This cohomology turns out to be canonically isomorphic with the local
(relative) cohomology of A. Grothendieck and M. Sato so that it provides
a handy way of representing the latter.
In this talk we present the theory of relative Dolbeault cohomology and
give, as applications, simple explicit expressions of Sato
hyperfunctions, some fundamental operations on them and related local
duality theorems. Particularly noteworthy is that the integration of
hyperfunctions in our framework, which is a descendant of the integration
theory on the Cech-de Rham cohomology, is simply given as the usual
integration of Stokes type. Also the Thom class in relative de Rham
cohomology plays an essential role in the scene of interaction between
topology and analysis.
The talk includes a joint work with N. Honda and T. Izawa. |

05/11/18 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Higher brackets on cyclic and negative cyclic (co)homology In this talk, we will embed the string topology bracket developed by Chas-Sullivan and Menichi on negative cyclic cohomology groups as well as the dual bracket found by de Thanhoffer de Voelcsey-Van den Bergh on negative cyclic homology groups into the global picture of a noncommutative differential (or Cartan) calculus up to homotopy on the (co)cyclic bicomplex in general, in case a certain Poincar´ duality is given. For negative cyclic cohomology, this in particular leads to a Batalin-Vilkovisky algebra structure on the underlying Hochschild cohomology. In the special case in which this BV bracket vanishes, one obtains an e_3-algebra structure on Hochschild cohomology. The results are given in the general and unifying setting of (opposite) cyclic modules over (cyclic) operads.
All this is joint work with D. Fiorenza. | ||

05/11/18 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Spherical functions and orthogonal polynomials I will explain how some questions we asked a few years ago on the multiplication of spherical functions on symmetric spaces are related to the so-called linearization problem for a certain kind of orthogonal polynomials, namely Jacobi polynomials. I will state some conjectures in the particular case of Jack polynomials. | ||

31/10/18 | Seminario | 16:00 | 17:00 | 1201 Dal Passo | Maria Stella Adamo | Università di Catania | The problem of continuity for representable functionals on Banach quasi
*-algebras.
A way to study problems concerning Quantum Statistical Mechanics is to
consider locally convex quasi ?-algebras, for which Banach quasi
?-algebras constitute a special class. For example, Banach quasi
?-algebras can be obtained by taking the completion of a ?-algebra A_0
with respect to a norm for which the multiplication is (only) separately
continuous.
In the (locally convex) quasi *-algebras setting, a relevant role is
played by representable functionals. Roughly speaking a linear
functional will be called representable if it allows a GNS-like
construction.
In this talk, we discuss about the problem of continuity for these
functionals and some related results. We begin our discussion by looking
at the the properties of representable (and continuous) functionals,
especially in the simplest case of Hilbert quasi *-algebras. This
discussion leads naturally to look at the problem of continuity for
these functionals, because no example of representable discontinuous
functional is known until now. Hence, we examine the approaches to study
this problem and the results about it. If the time permits, we will
discuss about future directions and applications. Joint work with C. Trapani |