18 Aprile, 2018 12:15

Seminari di Cultura Matematica

Ricostruire l'invisibile...fantasmi permettendo

Paolo Dulio, Politecnico di Milano

Politecnico di Milano Campus Bonardi Edificio14 aula B21

18 Aprile, 2018 15:15

Sezione di Analisi

Monotonicity formulas in potential theory with applications

Lorenzo Mazzieri, Università degli Studi di Trento

Aula seminari 3° piano

abstract

abstract

We present an overview of some new monotonicity formulas, holding in the realm of linear and nonlinear potential theory, together with their main applications to several domains of investigation. These are ranging from the theory of overdetermined boundary value problems in the classical Euclidean setting, to the classification of static black holes in general relativity and to the geometry of manifolds with nonnegative Ricci curvature. (Joint works with V. Agostiniani, M. Fogagnolo and A. Pinamonti).

17 Aprile, 2018 15:15

Sezione di Analisi

Nonlinear scalar field equations with competing potentials

Riccardo Molle, Università di Roma "Tor Vergata"

Aula 6° piano

abstract

abstract

In this talk a class of nonlinear elliptic equations on R^N is presented. These equations come from physical problems, where a potential interacts with the bumps in the solutions. We first discuss the interactions and present some old and new results; then we consider competing potentials, showing in particular a theorem on the existence of infinitely many positive bound state solutions. Finally, we present some examples on existence/non existence of a ground state solution, when the theorem applies.

12 Aprile, 2018 14:00

MOX Colloquia

Mixed finite elements and adaptive schemes for eigenvalue problems

Daniele Boffi, Dipartimento di Matematica "F. Casorati", Università di Pavia

Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

abstract

abstract

We review a posteriori error analysis and adaptive schemes for the approximation of eigenvalue problems arising from partial differential equations. Our ultimate goal is the design of adaptive schemes for the approximation of the eigenmodes associated with Maxwell's equations. It is well known that the Maxwell eigenvalue problem can be analyzed with the help of suitable mixed formulations. Taking advantage of this remark, we can prove the convergence with optimal rate for the edge finite element approximation of the Maxwell eigenvalue problem. In
three dimensions, the result is not a trivial extension of the analysis previously performed for the approximation of the Laplace eigenproblem in mixed form. Particular attention is paid to the case of multiple eigenvalues and clusters of eigenvalues.

Contact: christian.vergara@polimi.it

Daniele Boffi is professor of Numerical Analysis at the University of Pavia. His research focuses on the finite element discretization of partial differential equation with particular emphasis on mixed finite
elements. In particular, he is working on computational fluid dynamics, computational electromagnetism, and fluid-structure interactions. He is Director of the Doctoral School of the University of Pavia.

12 Aprile, 2018 14:30 in punto

Sezione di Geometria, Algebra e loro applicazioni

Non-canonical embeddings and a canonical torsion-free covering for Mori Dream Spaces

Michele Rossi, Università di Torino

Aula seminari del terzo piano

abstract

abstract

The talk will be divided in two parts, approximately 45 minutes each; the first part is intended to be an introduction to the more technical second part; there will be a brief break between the two parts.
In the first part of this talk I will recall a standard construction of an (almost)-canonical toric embedding of a (non-necessarily projective) Mori Dream Space (MDS), starting from its Cox ring. Moreover I will recall some notation about the GKZ-decomposition of the pseudo-effective and the moving cone of a MDS. In the second part we will see some obstruction to extending Hu-Keel birational geometric results to the non-projective setup. Then I will show how recent results, jointly obtained with L. Terracini for $\Q$-factorial complete toric varieties, can be easily extended to a general MDS, producing a projective embedding of every MDS of Picard number less than or equal to 2 and a canonical covering space, unramified in codimension 1, of a given MDS, which is still a MDS admitting a torsion-free class group.
In principle, an application of such a covering construction is that the Cox ring of a MDS, which is in general graded over a class group with non trivial torsion part, could be described in terms of the Cox ring of its canonical covering, which is now graded over a torsion-free class group. This is a work in progress.

Daniele Boffi is professor of Numerical Analysis at the University of Pavia. His research focuses on the finite element discretization of partial differential equation with particular emphasis on mixed finite
elements. In particular, he is working on computational fluid dynamics, computational electromagnetism, and fluid-structure interactions. He is Director of the Doctoral School of the University of Pavia.

11 Aprile, 2018 12:15

Seminari di Cultura Matematica

Cosa possono insegnarci i Bitcoin?

Matteo Bedini, Numerix

Politecnico di Milano Campus Bonardi Edificio14 aula B21

The talk will be divided in two parts, approximately 45 minutes each; the first part is intended to be an introduction to the more technical second part; there will be a brief break between the two parts.
In the first part of this talk I will recall a standard construction of an (almost)-canonical toric embedding of a (non-necessarily projective) Mori Dream Space (MDS), starting from its Cox ring. Moreover I will recall some notation about the GKZ-decomposition of the pseudo-effective and the moving cone of a MDS. In the second part we will see some obstruction to extending Hu-Keel birational geometric results to the non-projective setup. Then I will show how recent results, jointly obtained with L. Terracini for $\Q$-factorial complete toric varieties, can be easily extended to a general MDS, producing a projective embedding of every MDS of Picard number less than or equal to 2 and a canonical covering space, unramified in codimension 1, of a given MDS, which is still a MDS admitting a torsion-free class group.
In principle, an application of such a covering construction is that the Cox ring of a MDS, which is in general graded over a class group with non trivial torsion part, could be described in terms of the Cox ring of its canonical covering, which is now graded over a torsion-free class group. This is a work in progress.

Daniele Boffi is professor of Numerical Analysis at the University of Pavia. His research focuses on the finite element discretization of partial differential equation with particular emphasis on mixed finite
elements. In particular, he is working on computational fluid dynamics, computational electromagnetism, and fluid-structure interactions. He is Director of the Doctoral School of the University of Pavia.

11 Aprile, 2018 11:15

Sezione di Analisi

Nonlinear Schrödinger equations on branched structures: the role of topology in the existence of ground states

Enrico Serra, Politecnico di Torino

Aula seminari 3° piano

abstract

abstract

We describe some results on the existence or nonexistence of ground states of prescribed mass for the nonlinear Schrödinger equation on noncompact metric graphs. We will highlight the role played by the topology of the graph in all the existence results, in the cases of L^2 subcritical and critical power nonlinearity. In particular, in the critical case, a key role is played by a thorough analysis of the Gagliardo-Nirenberg inequalities on metric graphs and by estimates of their best constants. Most of the techniques are new and suited to the investigation of variational problems on metric graphs.

Daniele Boffi is professor of Numerical Analysis at the University of Pavia. His research focuses on the finite element discretization of partial differential equation with particular emphasis on mixed finite
elements. In particular, he is working on computational fluid dynamics, computational electromagnetism, and fluid-structure interactions. He is Director of the Doctoral School of the University of Pavia.

10 Aprile, 2018 12:15 in punto

Sezione di Finanza Quantitativa

The Black-Litterman Model and Views from a Reverse Optimization Procedure: An Out-of-Sample Performance Evaluation

Erindi Allaj, Università degli Studi di Firenze

Aula Seminari del Terzo Piano

abstract

abstract

The Black-Litterman (BL) model has been proposed as a valid solution to the problem of the estimation error in the parameter estimates of the Mean-Variance (MV) model. However, very little research has been done in order to facilitate the application of the BL model and to empirically test the performance of the BL model. The paper contributes to the existing literature by proposing an intuitive and easy application of the BL model. To this purpose, we suggest a novel approach to specify the investors views in the BL model. These views are derived by using a reverse optimization procedure similar to that used by the BL model in deriving the implied equilibrium expected excess returns. The second issue is addressed by empirically examining the out-of-sample performance of the BL model with respect to other asset allocation strategies. These strategies are given by the Sample MV (SMV), Minimum-Variance (MinV), Naive, Risk-Parity (RP), Capital Asset Pricing Model (CAPM), Strategic and the Bayesian strategy. In our empirical analysis, we also consider the reformulated BL model proposed by Allaj (2013) (BLEA model). Overall our results suggest that the BL model is a valid asset allocation strategy.

Daniele Boffi is professor of Numerical Analysis at the University of Pavia. His research focuses on the finite element discretization of partial differential equation with particular emphasis on mixed finite
elements. In particular, he is working on computational fluid dynamics, computational electromagnetism, and fluid-structure interactions. He is Director of the Doctoral School of the University of Pavia.

28 Marzo, 2018 12:15

Seminari di Cultura Matematica

The Spatial Organisation of Early Southeast Asian Landscapes: New Perspectives from Lidar

Damian Evans, École française d'Extrême-Orient

Politecnico di Milano Campus Bonardi Edificio14 aula B21

The Black-Litterman (BL) model has been proposed as a valid solution to the problem of the estimation error in the parameter estimates of the Mean-Variance (MV) model. However, very little research has been done in order to facilitate the application of the BL model and to empirically test the performance of the BL model. The paper contributes to the existing literature by proposing an intuitive and easy application of the BL model. To this purpose, we suggest a novel approach to specify the investors views in the BL model. These views are derived by using a reverse optimization procedure similar to that used by the BL model in deriving the implied equilibrium expected excess returns. The second issue is addressed by empirically examining the out-of-sample performance of the BL model with respect to other asset allocation strategies. These strategies are given by the Sample MV (SMV), Minimum-Variance (MinV), Naive, Risk-Parity (RP), Capital Asset Pricing Model (CAPM), Strategic and the Bayesian strategy. In our empirical analysis, we also consider the reformulated BL model proposed by Allaj (2013) (BLEA model). Overall our results suggest that the BL model is a valid asset allocation strategy.

Daniele Boffi is professor of Numerical Analysis at the University of Pavia. His research focuses on the finite element discretization of partial differential equation with particular emphasis on mixed finite
elements. In particular, he is working on computational fluid dynamics, computational electromagnetism, and fluid-structure interactions. He is Director of the Doctoral School of the University of Pavia.

21 Marzo, 2018 12:15

Seminari di Cultura Matematica

Crescita, Instabilità e Asimmetrie nei Sistemi Economici

Fabio Pammolli, Politecnico di Milano

Politecnico di Milano Campus Bonardi Edificio14 aula B21

The Black-Litterman (BL) model has been proposed as a valid solution to the problem of the estimation error in the parameter estimates of the Mean-Variance (MV) model. However, very little research has been done in order to facilitate the application of the BL model and to empirically test the performance of the BL model. The paper contributes to the existing literature by proposing an intuitive and easy application of the BL model. To this purpose, we suggest a novel approach to specify the investors views in the BL model. These views are derived by using a reverse optimization procedure similar to that used by the BL model in deriving the implied equilibrium expected excess returns. The second issue is addressed by empirically examining the out-of-sample performance of the BL model with respect to other asset allocation strategies. These strategies are given by the Sample MV (SMV), Minimum-Variance (MinV), Naive, Risk-Parity (RP), Capital Asset Pricing Model (CAPM), Strategic and the Bayesian strategy. In our empirical analysis, we also consider the reformulated BL model proposed by Allaj (2013) (BLEA model). Overall our results suggest that the BL model is a valid asset allocation strategy.

Daniele Boffi is professor of Numerical Analysis at the University of Pavia. His research focuses on the finite element discretization of partial differential equation with particular emphasis on mixed finite
elements. In particular, he is working on computational fluid dynamics, computational electromagnetism, and fluid-structure interactions. He is Director of the Doctoral School of the University of Pavia.