### Seminari

### Prossimi Seminari

**Computational Prediction of Blood Damage**

Marek Behr, Chair for Computational Analysis of Technical Systems Faculty of Mechanical Engineering, RWTH Aachen

lunedì 1 ottobre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Caputo Evolution Equations with time-nonlocal initial condition**

Lorenzo Toniazzi, University of Warwick

martedì 9 ottobre 2018 alle ore 15:15, Aula Seminari 3° piano**Statistical modeling and monitoring of product and process quality in Additive Manufacturing: opportunities and challenges**

Bianca Maria Colosimo, Dipartimento di Meccanica, Politecnico di Milano

giovedì 11 ottobre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Elastic waves in soft tissues: inverse analysis, experiments, simulations, validation**

Michel Destrade, Chair of Applied Mathematics at NUI Galway

giovedì 18 ottobre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**An overview of some mathematical and computational problems in Network Science**

Michele Benzi, Scuola Normale Superiore, Pisa

giovedì 22 novembre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**BIRATIONAL EQUIVALENCE OF ALGEBRAIC VARIETIES**

Shigefumi Mori, Kyoto University Institute of Advanced Study

lunedì 26 novembre 2018 alle ore 16:30, Aula Chisini, Diparimento di Matematica, Via C. Saldini 50

### Seminari Passati

**Ricostruire l’invisibile…fantasmi permettendo**

Paolo Dulio, Politecnico di Milano

mercoledì 18 aprile 2018 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Monotonicity formulas in potential theory with applications**

Lorenzo Mazzieri, Università degli Studi di Trento

mercoledì 18 aprile 2018 alle ore 15:15, Aula seminari 3° pianoABSTRACTWe 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).**Nonlinear scalar field equations with competing potentials**

Riccardo Molle, Università di Roma “Tor Vergata”

martedì 17 aprile 2018 alle ore 15:15, Aula 6° pianoABSTRACTIn 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.**Mixed finite elements and adaptive schemes for eigenvalue problems**

Daniele Boffi, Dipartimento di Matematica “F. Casorati”, Università di Pavia

giovedì 12 aprile 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANOABSTRACTWe 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

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

Michele Rossi, Università di Torino

giovedì 12 aprile 2018 alle ore 14:30 precise, Aula seminari del terzo pianoABSTRACTThe 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.

**Cosa possono insegnarci i Bitcoin?**

Matteo Bedini, Numerix

mercoledì 11 aprile 2018 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Nonlinear Schrödinger equations on branched structures: the role of topology in the existence of ground states**

Enrico Serra, Politecnico di Torino

mercoledì 11 aprile 2018 alle ore 11:15, Aula seminari 3° pianoABSTRACTWe 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.**The Black-Litterman Model and Views from a Reverse Optimization Procedure: An Out-of-Sample Performance Evaluation**

Erindi Allaj, Università degli Studi di Firenze

martedì 10 aprile 2018 alle ore 12:15 precise, Aula Seminari del Terzo PianoABSTRACTThe 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.