Sala Seminari (Dip. Matematica)
In this talk, I will present some results in collaboration with L. Abatangelo
(Milano-Bicocca), L. Hillairet (Orléans), C. Léna (Torino), B. Noris
(Amiens), M. Nys (Torino), concerning the behavior of the eigenvalues of
Aharonov-Bohm operators with one moving pole or two colliding
poles. In both cases of poles moving inside the domain and approaching
the boundary, the rate of the eigenvalue variation is estimated in
terms of the vanishing order of some limit eigenfunction. An accurate
The most common methods to compute roots of polynomials is to rephrase the problem in linear algebra terms: one constructs a companion matrix (or pencil) that has the roots of the polynomial as eigenvalues.
However, even when the eigenvalue method used is backward stable, it's non-trivial to map the backward error back on the polynomial. This problem has been studied extensively in the past and it has been shown that relying on the QR method does not provide a normwise backward-stable rootfinder. For this reason, one needs to rely on QZ + appropriate scaling.
Dato un fascio coerente F su una varieta' liscia proiettiva X, viene determinata l'algebra di Lie differenziale graduata che controlla le deformazioni della coppia (X,F). Viene poi introdotto un morfismo di traccia tra opportuni fasci di operatori differenziali mediante il quale viene esteso un classico risultato di Artamkin sulle deformazioni di fasci.
Given a closed 3-manifold Y with the action of a finite group G, we show how to find a closely related hyperbolic G-manifold Y’. The two manifolds are related by an invertible equivariant homology cobordism; a cobordism from Y to Y’ is invertible if there is a second cobordism from Y’ to Y such that the union of the two along Y’ is a product cobordism. I will give a collection of applications in 3 and 4-dimensional topology. (Joint work with Dave Auckly, Hee Jung Kim, and Paul Melvin.)