Sala Seminari (Dip. Matematica)

Willmore Flow of Networks

Abstract. We consider networks of curves in the plane moving according to the L^2-gradient flow of a variant of the elastic energy. In this talk we will prove short time existence in the case of networks composed by three curves that are required to meet in one or two triple junctions. As a variation of the result we additionally impose that they form an angle of 120 degrees at the triple junction(s). If time allows we will give some outlook on our expectations concerning the long time behaviour based on numerical work by John Barrett, Harald Garcke and Robert Nürnberg.
Data Seminario: 
Wednesday, November 29, 2017
Relatore: 
Julia Menzel
Ora Fine: 
Saturday, January 1, 0000 - 19:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 18:00

Minimal Elastic Networks

Abstract. In this talk we will consider planar networks of three curves minimizing a combination of the elastic energy and the length functional. We will prove existence and regularity of minimizers and we will show some properties of the minimal configurations. In addition to the presentation of the results that are obtained in collaboration with Anna Dall'Acqua and Matteo Novaga, we will give a partial review of the theory of elasticae and discuss about the onset of new phenomena passing from the problem for curves to the one for networks.
Data Seminario: 
Wednesday, November 29, 2017
Relatore: 
Alessandra Pluda
Ora Fine: 
Saturday, January 1, 0000 - 18:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 17:00

Functions of fractal bounded variation

Abstract. In this talk we introduce a notion of functions of fractal bounded variation. Here, the sup-norm of test functions as used in the classical definition is replaced by the Hoelder norm with respect to some exponent. Characteristic functions of domains with fractal bounderies are particular examples that belong to this class. Among a characterization in terms of currents, we state some properties that naturally extend those of classical BV functions such as higher integrability, decomposition into Hoelder functions and push forwards.
Data Seminario: 
Wednesday, November 22, 2017
Relatore: 
Roger Züst
Ora Fine: 
Saturday, January 1, 0000 - 19:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
Saturday, January 1, 0000 - 18:00

Seminario di Algebra e Teoria dei numeri - Solvable primitive extensions

Relatore: 
Chandan Dalawat

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.

Data Seminario: 
Friday, December 1, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
Saturday, January 1, 0000 - 15:30
Affiliazione: 
Harish-Chandra Research Institute
Ora Inizio: 
Saturday, January 1, 0000 - 14:00

Optimal partitions.

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

Variational approximations and relaxations of the Steiner problem

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

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

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