### Seminari

### Prossimi Seminari

**Models, Simulation, Uncertainty, and Medicine – Numerical Methods in Computational Biomechanics and Cardiology**

Rolf Krause, Center for Computational Medicine in Cardiology, Università della Svizzera italiana,

giovedì 22 febbraio 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Sobolev and BV functions in infinite dimension**

Alessandra Lunardi, Università di Parma

venerdì 23 febbraio 2018 alle ore 10:30 precise, Sala Consiglio, 7 piano, Edificio La Nave, Via Bonardi 9**How to eliminate/control flutter arising in flow structure interactions**

Irena Lasiecka, University of Memphis

mercoledì 28 febbraio 2018 alle ore 16:30, Sala Consiglio, 7 piano, Edificio La Nave, Via Bonardi 9**Graphene from Molecular Mechanics**

Ulisse Stefanelli, Faculty of Mathematics, University of Vienna, and CNR Pavia

giovedì 1 marzo 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Post-Quantum Group-based Cryptography**

Delaram Kahrobaei, New York City College of Technology

giovedì 8 marzo 2018 alle ore 14:30 precise, Aula seminari, III piano, Dipartimento di matematica**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**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**Cosa possono insegnarci i Bitcoin?**

Matteo Bedini, Numerix

mercoledì 11 aprile 2018 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**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 MILANO**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**Computing disconnected bifurcation diagrams of partial differential equations**

Patrick Farrell, Mathematical Institute, Oxford

giovedì 26 aprile 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Computer, simulazioni ed esperimenti: all’alba di un nuovo metodo sperimentale?**

Viola Schiaffonati, Politecnico di Milano

mercoledì 9 maggio 2018 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Modellazione paziente specifica in emodialisi**

Maria Laura Costantino, Politecnico di Milano

mercoledì 16 maggio 2018 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**La Scoperta del Secolo – Perché le Onde Gravitazionali valgono un Nobel**

Luca Perri, L’Officina del Planetario

mercoledì 23 maggio 2018 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**La geometria delle piramidi egizie**

Corinna Rossi, Politecnico di Milano

mercoledì 30 maggio 2018 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Missione Planck, l’immagine dell’universo neonato**

Marco Bersanelli, Università degli Studi di Milano

mercoledì 6 giugno 2018 alle ore 12:15, Politecnico di Milano Campus Bonardi Edificio14 aula B21**Joint and Individual Variation Explained**

Steve Marron, Department of Statistics and O.R., University of North Carolina

lunedì 18 giugno 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

### Seminari Passati

**Poincaré-Sobolev Inequalities and the p-Laplacian**

Scott Rodney, Cape Breton University

mercoledì 21 febbraio 2018 alle ore 15:15, Aula seminari 3° pianoABSTRACTIt is well known that Poincar\’e-Sobolev inequalities play an important role in applications and in regularity theory for weak solutions of PDEs. In this talk I will discuss two new results connecting matrix weighted Poincar\’e-Sobolev estimates to the existence of regular weak solutions of Dirichlet and Neumann problems for a degenerate $p$-Laplacian:

\begin{eqnarray}

\Delta_{Q,p} \varphi(x) = \textrm{Div}\left(\big|Q(x)~\nabla \varphi(x)\big|^{p-2}~Q(x)~\nabla\varphi(x)\right).\nonumber

\end{eqnarray}

Degeneracy of $\Delta_{Q,p}$ is given by a measurable non-negative definite matrix-valued function $Q(x)$.**Numerical modelling of elliptic problems on octree-based meshes**

Alice Raeli, IMAG Institut Montpelliérain Alexander Grothendiec, Montpellier

mercoledì 21 febbraio 2018 alle ore 10:00, Aula Saleri VI Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANOABSTRACTWe consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The gradient of the solution can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure.Numerical illustrations are presented in two and three-dimensional configurations. Future perspectives will include the use of Hybrid High-Order methods to increase the approximation order.

Contact: luca.formaggia@polimi.it

**Realized Peaks over Threshold: a Time-Varying Extreme Value Approach with High-Frequency based Measures**

Luca Trapin, Scuola Normale Superiore

martedì 20 febbraio 2018 alle ore 12:15 precise, Aula seminari terzo piano**Elastic Contact in Fluid-structure Interactions**

Thomas Richter, Universität Magdeburg

lunedì 19 febbraio 2018 alle ore 14:00, Aula Saleri VI Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANOABSTRACTIn this talk we address the following fundamental question: what happens if an elastic ball is falling in a container with a viscous fluid towards a rigid wall on the bottom? Will it come to contact? Or will there always remain a thin fluid film between wall and bottom? Will the ball bounce off? Or will the ball come to rest and stick? We start by giving an overview on various results on this topic, computationally, analytically and experimentally. Then in a second part we numerically investigate this challenging problem.

The possible contact between ball and boundary is a fundamental difficulty for established discretization schemes as it involves topology changes in the domain. For describing the interaction problem between elastic solid and fluid we shortly introduce the ALE approach and discuss its shortcomings in terms of modeling contact. Then, we introduce an alternative Eulerian approach that is well suited for contact problems. This Eulerian approach however brings along new difficulties with respect to discretization.

Contact: christian.vergara@polimi.it

**Understanding Heart Tissue through Waves**

D. Nordsletten, Biomedical Engineering Department, King’s College, London

giovedì 15 febbraio 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANOABSTRACTPersonalised models of cardiac mechanics have evolved into a powerful tool for studying the human heart in health and disease. Combining detailed information on the heart kinematics extracted from medical images, with mathematical models of cardiac function, patient-specific models provide a mathematical representation of individual hearts. As model parameters are linked to intrinsic tissue properties such as stiffness and contractility, unique and accurate parameter estimates are a prerequisite for the potential translation of personalised models to the clinic.

In parallel, magnetic resonance elastography (MRE) has evolved into a powerful tool for interrogating material stiffness. MRE has been exploited in the liver, breast, and brain using measured periodic waves to extract material stiffness properties. Transducing waves via external vibrations, MRE provides a more direct measure of the characteristics of tissues and their potential diseases. Integrating this work into the heart is complicated by a myriad of challenges including the inherent cardiac motion of the heart, evolving material properties due to the contractile state of the muscle, and the nonlinear effects of deformation on the apparent stiffness of the material.

In this talk, we discuss the merger of these two worlds, bridging between the nearly quasi-static model-based assessment of heart function and the high frequency wave-based assessment. In particular, we discuss the simple influence of deformation on apparent stiffness, explaining both from the realm of traditional wave mechanics and biomechanical theory.

Contact: christian.vergara@polimi.it

**Macroscopic quantum systems & Measuring apparatuses**

Caterina Foti, Università degli Studi di Firenze

martedì 13 febbraio 2018 alle ore 14:30 precise, Aula Seminari III pianoABSTRACTThe emergence of classicality is the mechanism that makes us to observe a classical reality despite the fundamental laws of physics being quantum.

Apart from the neverending diatribe between different interpretations of Quantum Mechanics, what can be considered more or less accepted is that we experience a classical reality due to the continuos interaction between each microscopic component of any physical system and its environment, that can be regarded as the measuring apparatus and must be macroscopic since it contains us as observers. Among the various approaches proposed over the years by different authors to deal with the “quantum-to-classical” crossover, a useful tool is provided by the general method introduced by L. G. Yaffe in 1982 for finding the classical limits as large-N limits of arbitrary quantum theories with N dynamical variables. Such method isolates the minimal structure that any quantum theory should possess in order to have a classical limit. By using Yaffe’s results in the framework of open quantum systems dynamics, one can show that whenever quantum environments have a sensible large-N limit, they evolve as if they were the same measuring apparatus in the classical limit.**Regularization Theory and Applications to Photoacoustic Imaging**

Otmar Scherzer, University of Vienna and Radon Institute of Computational and Applied Mathematics (Linz), Austria

giovedì 8 febbraio 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANOABSTRACTIn this talk we review recent results on regularization theory of variational regularization methods, such as Tikhonov regularization, which consists in finding the optimizer of a least functional which is perturbed by a convex functional. In particular we are reviewing new convergence rates results for solving Inverse Problemsin Hilbert Spaces.

Particular emphasize will be given to analyze and interpret the abstract results for photoacoustic imaging and inversion of the spherical mean operator.

Contact: elena.beretta@polimi.it

**Critical aspects of Choquard type equations**

Daniele Cassani, Università degli Studi dell’Insubria

mercoledì 7 febbraio 2018 alle ore 16:30, Aula seminari 3° pianoABSTRACTWe are concerned with a class of nonlocal Schroedinger equations which show up in many different applied contexts. In particular we consider the case in which the nonlinear interaction has critical features. In the classical Sobolev sense, when we are in presence of the Hardy-Littlewood-Sobolev upper-critical exponent, as well as new critical phenomena occur, the so-called ‘bubbling at infinity’, when the nonlinearity exhibits lower-critical growth. Assuming mild conditions on the nonlinearity and by using variational methods, we establish existence, non-existence and qualitative properties of finite energy solutions. Some partial results in the limiting case of dimension two will be also presented.

(Joint works in collaboration with: J. Zhang; J. Van Schaftingen and J. Zhang; C. Tarsi and M. Yang).