Sala Seminari (Dip. Matematica)

Optimizing the fractional power of a Diffusion operator

Abstract. We study an optimization problem with SPDE constraints, which has the peculiarity that the control parameter $s$ is the $s$-th power of the diffusion operator in the state equation. Before moving to the SPDE case, we first describe the result of Sprekels-Valdinoci for the PDE case. Then we discuss a suitable concept of solutions of the state equation and establish pathwise differentiability properties of the stochastic process w.r.t. the fractional parameter $s$. Finally, we show that under certain conditions on the noise, optimality conditions for
Data Seminario: 
Wednesday, April 26, 2017
Relatore: 
Carina Geldhauser
Ora Fine: 
0000 - 18:00
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
0000 - 17:00

Scalar conservation laws with discontinuous flux

Relatore: 
Francesco Ghiraldin
Abstract. In the talk I will investigate the uniqueness of solutions of scalar conservation laws with discontinuous flux. While in the smooth setting this property follows from Kruzhkov's entropy inequalities, in the case of discontinuous fluxes these inequalities are not enough and additional dissipation conditions must be imposed at the discontinuity set of the flux. I will explain how any entropy solution admits traces on the discontinuity set of the flux field and use this to prove the validity of a generalized Kato inequality for any pair of solutions.
Data Seminario: 
Wednesday, May 3, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 18:00
Affiliazione: 
Max Planck Institute Leipzig
Ora Inizio: 
0000 - 17:00

Numerical study of 1D optimal structures

Relatore: 
Edouard Oudet
Abstract. We focus our attention on shape optimization problems in which one dimensional connected objects are involved. Very old and classical problems in calculus of variation are of this kind: euclidean Steiner's tree problem, optimal irrigation networks, cracks propagation, etc. In a first part we quickly recall some previous work in collaboration with F. Santambrogio related to the functional relaxation of the irrigation cost. We establish a $\Gamma$-convergence of Modica and Mortola's type and illustrate its efficiency from a numerical point of
Data Seminario: 
Wednesday, April 19, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 19:00
Affiliazione: 
Université Grenoble Alpes
Ora Inizio: 
0000 - 18:00

Embedding arithmetic hyperbolic manifolds

Tipo Seminario: 
Relatore: 
Leone Slavich

Given an n-dimensional hyperbolic manifold M, it is reasonable to ask whether or not it can be realized as a totally geodesic, embedded submanifold of an (n+1)-dimensional hyperbolic manifold. If this is true, we say that M geodesically embeds. Determining whether or not a hyperbolic manifolds geodesically embeds is, in general, quite difficult.

However, if we restrict our attention to the case of arithmetic manifolds of simplest type, (a class of manifolds constructed using tools from number theory), we can show that, in many cases, they do indeed embed geodesically.

Data Seminario: 
Wednesday, April 5, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 16:00
Affiliazione: 
Università di Pisa
Ora Inizio: 
0000 - 15:00

Seminario di Teoria dei numeri - On some algebraic properties of the locally free class group

Relatore: 
Dott.Reynold Fregoli

Abstract:
Let N/K be a normal tame extension of number fields and let G := Gal(N/K)
be its Galois group. It is common knowledge that, under these conditions,
[O_N] lies in the locally free class group Cl(O_K[G]). What can be said about
the existence of a normal integral basis for the extension N/K, by knowing
the structure of the group Cl(O_K[G])? In some cases this problem is easily
settled via cancellation law.
There is also a rank notion for locally free modules over orders. Which

Data Seminario: 
Tuesday, April 4, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Inizio: 
0000 - 16:00
Ora Fine: 
0000 - 17:00

Topological and holomorphic disk filling

Relatore: 
Roberta Maccheroni

In this talk I’ll describe the problem of filling submanifolds with topological or holomorphic disks. The case of geodesics on compact Riemannian surfaces with nonpositive scalar curvature will be treated. I will prove non existence of such disk filling, using several different tecniques. Two possible generalizations in higher dimension will be shown:

– the product of geodesics on the product of compact Riemannian surfaces with nonpositive scalar curvature does not admit a holomorphic disk filling;

Data Seminario: 
Friday, March 31, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 15:30
Affiliazione: 
Università di Parma
Ora Inizio: 
0000 - 14:30

Some results on focusing Mean Field Games

Relatore: 
Marco Cirant
Abstract. Mean Field Game (MFG) theory is the study of strategic decision making in a very large population of small interacting individuals. We consider models where agents prefer clustering in high-density areas. The goal is to understand the existence of smooth solutions to the corresponding MFG system of coupled ergodic Hamilton-Jacobi-Bellman and Kolmogorov equations.
Data Seminario: 
Wednesday, April 19, 2017
Aula: 
Sala Seminari (Dip. Matematica)
Ora Fine: 
0000 - 18:00
Affiliazione: 
Universita' di Padova
Ora Inizio: 
0000 - 17:00

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