# Sala Seminari (Dip. Matematica)

## Optimal Interpolation Formulas in W_2^{(m,m-1)} space

In this talk, using S.L.Sobolev’s method, optimal interpolation formulas are constructed in *W_{2} ^*(*m,m**−*1) (0*,*1) space. Explicit formulas for coefficients of optimal interpolation formulas are obtained. Some numerical results are presented.

## Minimal volume hyperbolic 4-manifolds

Since the volume of a hyperbolic manifold is often regarded as a measure of its complexity, it is interesting to study the examples of minimal volume.

The 2 and 3-dimensional cases are well understood.

In dimension four there is an abundance of examples, but we are far from classifying them. In this talk, we will survey all known examples of minimal volume hyperbolic 4-manifolds and prove that these fall into three commensurability classes. This is joint work with Stefano Riolo.

## A Hele-Shaw tumor growth model as a gradient flow.

## On Aharonov-Bohm operators with moving poles

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 saga of a fish: from a survival guide to closing lemmas for dynamical systems

## Some large deviations results

## Liouville-type problems on compact surfaces: a variational approach

## Backward error analysis for polynomial rootfinders

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.