## 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.

Tipo Seminario:

Relatore:

Edouard Oudet

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.

Data Seminario:

Wednesday, December 13, 2017

Aula:

Sala Seminari (Dip. Matematica)

Ora Fine:

Saturday, January 1, 0000 - 18:00

Affiliazione:

Centro De Giorgi

Ora Inizio:

Saturday, January 1, 0000 - 17:00

Tipo Seminario:

Relatore:

Mauro Bonafini

Abstract. In this talk we focus our attention on problems involving one dimensional sets, using as guiding example the Euclidean Steiner tree problem. We first reformulate the problem over a suitable family of rank one tensor valued measures and then we take two different perspectives. In the first case we focus on the planar setting and provide a variational approximation via Gamma convergence by means of functionals of phase transition type.

Data Seminario:

Wednesday, December 6, 2017

Aula:

Sala Seminari (Dip. Matematica)

Ora Fine:

Saturday, January 1, 0000 - 18:00

Affiliazione:

Universita' di Trento

Ora Inizio:

Saturday, January 1, 0000 - 17:00

Tipo Seminario:

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

Tipo Seminario:

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

Tipo Seminario:

Relatore:

Samandar Babaev

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.

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

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

Tipo Seminario:

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

Tipo Seminario:

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

Tipo Seminario:

Relatore:

Eugene Stepanov

Abstract.

Data Seminario:

Wednesday, October 25, 2017

Aula:

Sala Seminari (Dip. Matematica)

Ora Fine:

Saturday, January 1, 0000 - 19:00

Affiliazione:

St. Petersburg State University

Ora Inizio:

Saturday, January 1, 0000 - 18:00

Data Seminario:

Friday, February 16, 2018

Relatore:

Prof.Claudio Macci

Aula:

Sala Seminari (Dip. Matematica)

Ora Inizio:

Saturday, January 1, 0000 - 10:00

Ora Fine:

Saturday, January 1, 0000 - 11:00