Sala Seminari (Dip. Matematica)

Asymptotic planar N-bubble

Relatore: 
Giacomo Del Nin
Abstract. We consider in the plane a fixed finite number N of "bubbles", that is disjoint finite perimeter sets which possibly share portions of their boundaries, and look for configurations that minimize, under a volume constraint, the total weighted length of their boundaries: the interface between each bubble and the exterior is given weight 1 while the interface between any two bubbles is given weight $2-\varepsilon$. We are interested in the case when $\epsilon$ converges to 0: we prove that minimizing
Data Seminario: 
Wednesday, November 22, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Universita' di Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Branched transportation: stability and new models.

Relatore: 
Andrea Marchese
Abstract. Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree, or the nervous and the cardiovascular systems. Given a flow that transports a given mass distribution $\mu^-$ onto a target distribution $\mu^+$, along a 1-dimensional network, the transportation cost per unit length is proportional to a concave power $\alpha \in (0,1)$ of the intensity of the flow. This favors grouping of the particles' trajectories and prevents diffusion.
Data Seminario: 
Wednesday, November 15, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
University of Zurich
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

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

Relatore: 
Samandar Babaev

In this talk, using S.L.Sobolev’s method, optimal interpolation formulas are constructed in W_{2} ^(m,m1) (0,1) space. Explicit formulas for coefficients of optimal interpolation formulas are obtained. Some numerical results are presented.

Data Seminario: 
Wednesday, November 8, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:00
Affiliazione: 
Bukhara State University, Uzbekistan
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

Minimal volume hyperbolic 4-manifolds

Tipo Seminario: 

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.
 

Data Seminario: 
Thursday, November 2, 2017
Relatore: 
Leone Slavich
Ora Fine: 
Saturday, January 1, 0000 - 16:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 15:00

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

Relatore: 
Simone Di Marino
Abstract. In 2014 Perthame, Quiroz and Vasquez unite two types of modeling of tumor growth into a unique framework of reaction-diffusion type where the diffusive term is $\Delta p(\rho)$ and $p(\rho)=\rho^m$. The stiff limit $m \to \infty$ is in particular a Hele-Shaw type problem: we find a gradient flow formulation of this problem, namely it is the gradient flow of the negative mass with respect to the Wasserstein-Fisher-Rao distance, discovered simultaneously by many authors in the last years.
Data Seminario: 
Wednesday, November 8, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Affiliazione: 
Scuola Normale Superiore
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

On Aharonov-Bohm operators with moving poles

Relatore: 
Veronica Felli

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

Data Seminario: 
Tuesday, November 7, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 14:00
Affiliazione: 
Università di Milano bicocca
Ora Inizio: 
Saturday, January 1, 0000 - 13:00

Liouville-type problems on compact surfaces: a variational approach

Abstract. A class of Liouville equations and systems on compact surfaces is considered: we focus on the Toda system which is motivated in mathematical physics by the study of models in non-abelian Chern-Simons theory and in geometry in the description of holomorphic curves. We discuss its variational aspects which yield existence results.
Data Seminario: 
Wednesday, October 25, 2017
Relatore: 
Aleks Jevnikar
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Backward error analysis for polynomial rootfinders

Relatore: 
Leonardo Robol

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.

Data Seminario: 
Tuesday, October 17, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 11:00
Affiliazione: 
ISTI--CNR Pisa
Ora Inizio: 
Saturday, January 1, 0000 - 10:00

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