### 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

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

Damian Evans, École française d’Extrême-Orient

mercoledì 28 marzo 2018 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Crescita, Instabilità e Asimmetrie nei Sistemi Economici**

Fabio Pammolli, Politecnico di Milano

mercoledì 21 marzo 2018 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**A representation formula for the Laplacian of the distance function**

Andrea Mondino, University of Warwick

mercoledì 21 marzo 2018 alle ore 15:15, Sala del Consiglio 7° pianoABSTRACTIn the seminar I will present a recent work in collaboration with Fabio Cavalletti (SISSA) where, using techniques from optimal transportation, we prove a rather explicit representation formula for the Laplacian of the distance function in spaces with Ricci curvature bounded below. Even if the paper deals with rather general non-smooth spaces, since some results seem new even for smooth manifolds, the seminar will be mostly focused on the smooth framework.**Collisions and chaos in the Boltzmann-Grad limit**

Sergio Simonella, ENS Lione

mercoledì 21 marzo 2018 alle ore 14:45 precise, Aula seminari MOX, VI pianoABSTRACTI will review our current state of knowledge on the mathematical derivation of the Boltzmann equation from Newtonian systems. This problem has been the objective of intensive effort over recent years. I will focus on the size of correlations in the dilute gas and discuss some delicate aspects of the convergence in the kinetic limit. A statistical analysis of collisions via analytical tools provides new insights on the scale transition.**“The Quantization approach for estimating Exposures in Counterparty risk. Review with numerical Applications”**

MICHELE BONOLLO, NUMERIX

martedì 20 marzo 2018 alle ore 12:15, Aula Seminari Sesto Piano**Isogeometric-analysis-based Multi-Index Stochastic Collocation for Elliptic PDEs with random data**

Lorenzo Tamellini, Istituto “E. Magenes”, Consiglio Nazionale delle Ricerche, Pavia

martedì 20 marzo 2018 alle ore 11:00, Aula Seminari ‘Saleri’ VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano – Edificio 14ABSTRACTIn many engineering applications governed by PDEs, the parameters of the equations (coefficients, forcing terms, boundary and initial conditions, shape of the domain) are not known exactly but rather affected by a certain degree of uncertainties, and can be described by means of random variables (or random fields).

Uncertainty Quantification (UQ) aims at estimating how the randomness of these “input” parameters affects the “outputs” of the PDE, typically its solution or functionals thereof. UQ techniques are often based on repeatedly solving the PDE at hand for different combinations of the input parameters (i.e., a sampling approach), which requires a significant computational effort.

To reduce such effort, so-called “multi-level” and “multi-index” methods have recently been proposed. These methods explore the variability of the PDE outputs using a hierarchy of suitably chosen discretization levels to balance the PDE discretization error and the sampling error, and refine the discretization of the PDE only when needed. We emphasize in particular that these methodologies are completely “black-box”, in the sense that they allow reuse of legacy PDE solvers, and are moreover

embarrassingly parallel.

In this talk we describe in detail one such method, i.e., the so-called Multi-Index Stochastic Collocation method (MISC), which is closely related to the quite popular Sparse-Grids Stochastic Collocation method for the approximation of PDE with random data.

In particular, this method relies on PDE solvers with tensor structure. To this end, we use Isogeometric Analysis (IGA), which is a technique introduced in the early 2000 to bridge the gap between Computer Aided Design (CAD) and PDE-based engineering analysis.

The core idea of IGA is to use the basis functions used by CAD designers to describe geometries (typically Cubic Splines or Non-Uniform Rational B-Splines) as a basis for the approximation of the solution of the PDE as well; the PDE is then solved a traditional Galerkin approach.

Beside the fact that its tensorized construction makes IGA very suitable in the MISC framework, attractive features of IGA are the simplified treatment of complex geometries, and the fact that basis functions with high-order and high-degree of regularity can be easily generated, thanks to the flexibility of the splines bases.

This is a joint work with Joakim Beck and Raul Tempone (KAUST), Abdul-Lateef Haji-Ali (Oxford) and Fabio Nobile (EPFL).

Contact: luca.formaggia@polimi.it

**One-Slice Preserving Functions of a Quaternionic Variable**

Chiara de Fabritiis, Università Politecnica delle Marche

giovedì 15 marzo 2018 alle ore 14:00 precise, Aula seminari del terzo pianoABSTRACTRegular functions on the skew-field of quaternions were introduced by

Gentili and Struppa some 10 years ago in order to give an analogue of

holomorphic functions in a non commutative setting. After a (short)

introduction, I will give a formula which allows us to simplify the

understanding of the *-product, which corresponds to the pointwise

product of holomorphic functions. The peculiar structure of quaternions,

foliated in copies of complex plane, drives naturally to consider the

classes of functions which preserve either one or all complex slices.

The main part of the talk will be devoted to characterize the functions

whose sum, *-product or conjugate preserve a slice. At the end, time permitting, I will address to the case of *-powers which shows an unexpected connection with a problem of algebraic geometry studied by Causa and Re. (Joint work with A. Altavilla)**The constant scalar curvature equation in some singular spaces**

Gilles Carron, Laboratoire de Mathématiques Jean Leray (UMR 6629), Université de Nantes, CNRS

mercoledì 14 marzo 2018 alle ore 16:30, Sala Consiglio, 7 piano, Edificio La Nave, Via Bonardi 9ABSTRACTI will survey the recent results about the Yamabe problem on stratified spaces. I will first introduce the scalar curvature and the Yamabe equation for the constant scalar curvature equation and its variational formulation and the results of Obata, Trudinger, Aubin and Schoen for smooth compact manifold. Then I will describe the geometry of stratified space with some 2D and 3D examples. Eventually I will formulate the Yamabe problem for stratified space and explained some of the recent results and will explain some perspectives.