# Sala Seminari (Dip. Matematica)

## Minimal Elastic Networks

## Functions of fractal bounded variation

## Seminario di Algebra e Teoria dei numeri - Solvable primitive extensions

**Abstract**: A finite separable extension E of a field F is called primitive if there are no intermediate extensions. It is called solvable if the group Gal(Ê |F) of automorphisms of its galoisian closure Ê over F is solvable. What are the solvable primitive extensions of F ? This problem goes back to Évariste Galois; we show how some recent work complements his insights.

## Optimal partitions.

ABSTRACT. We present recent numerical approaches dedicated to the identification

of optimal partitions associated to geometrical costs. We focus our

presentation on 2D surfaces and full 3D problems.

## Variational approximations and relaxations of the Steiner problem

## Asymptotic planar N-bubble

## Branched transportation: stability and new models.

## 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.