### 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

**Spectral distribution of sequences of structured matrices: GLT theory and applications**

Debora Sesana, University of Insubria – Como –

martedì 13 marzo 2018 alle ore 15:00, Aula Seminari ‘Saleri’ VI Piano MOX-Dipartimento di Matematica, Politecnico di Milano – Edificio 14ABSTRACTAny discretization of a given differential problem for some sequence of stepsizes h tending to zero leads to a sequence of systems of linear equations {Am xm = bm}, where the dimension of {Am} depends on h and tends to infinity for h going to 0. To properly face the solution of such linear systems, it is important to deeply understand the spectral properties of the matrices {Am} in order to construct efficient preconditioners and to study the convergence of applied iterative methods. The spectral distribution of a sequence of matrices is a fundamental concept. Roughly speak- ing, saying that the sequence of matrices {Am} is distributed as the function f means that the eigenvalues of Am behave as a sampling of f over an equispaced grid of the domain of f, at least if f is smooth enough. The function f is called the symbol of the sequence. Many distribution results are known for particular sequences of structured matrices: diagonal matrices, Toeplitz matrices, etc. and an approximation theory for sequences of matrices has been developed to deduce spectral distributions of “complicated” matrix sequences from the spectral distribution of “simpler” matrix sequences. In this respect, recently, has played a fundamental role the theory of Generalized Locally Toeplitz (GLT) sequences (introduced by Tilli (1998) and Serra-Capizzano (2002, 2006)), which allows to deduce the spectral properties of matrix sequences obtained as a combination (linear combinations, products, inversion) of Toeplitz matrices and diagonal matrices; to this category belong many stiffness matrices arising from the discretization, using various methods, of PDEs. We present the main concepts of this theory with some applications.

This is a joint work with Stefano Serra-Capizzano and Carlo Garoni.

References

[1] C. Garoni, C. Manni, S. Serra-Capizzano, D. Sesana, H. Speleers. Spectral analysis and spectral symbol of matrices in isogeometric Galerkin methods. Mathematics of Computation 85 (2016), pp. 1639–1680.

[2] C. Garoni, C. Manni, S. Serra-Capizzano, D. Sesana, H. Speleers. Lusin theorem, GLT sequences and matrix computations: an application to the spectral analysis of PDE discretization matrices. Journal of Mathematical Analysis and Applications, 446 (2017), pp. 365–382.

[3] C. Garoni, S. Serra-Capizzano. Generalized Locally Toeplitz Sequences: Theory and Applications. Springer 2017.

[4] C. Garoni, S. Serra-Capizzano, D. Sesana. Block Locally Toeplitz Sequences: Construction and Properties. Springer INdAM Series: proceeding volume of the Cortona 2017 meeting, submitted.

[5] C. Garoni, S. Serra-Capizzano, D. Sesana. Block Generalized Locally Toeplitz Sequences:

Topological Construction, Spectral Distribution Results, and Star-Algebra Structure.

Springer INdAM Series: proceeding volume of the Cortona 2017 meeting, submitted.

Contact: franca.calio@polimi.it

**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 matematicaABSTRACTThe National Security Agency (NSA) in August 2015 announced plans to transition to post-quantum algorithms “Currently, Suite B cryptographic algorithms are specified by the National Institute of Standards and Technology (NIST) and are used by NSA’s Information Assurance Directorate in solutions approved for protecting classified and unclassified National Security Systems (NSS). Below, we announce preliminary plans for transitioning to quantum resistant algorithms.”

Shortly after the National Institute of Standardization and Technology (NIST) announced a call to select standards for post-quantum public-key cryptosystems.

The academic and industrial communities have suggested as the quantum-resistant primitives: Lattice-based, Multivariate, Code-based, Hash-based, Isogeny-based and group-based primitives.

In this talk I will focus on some ideas of (semi)group-based primitives. The one which was proposed to NIST is by SecureRF company based in Connecticut, among its founders there is a number theorist (Goldfeld) and two group theorists (Anshel and Anshel). They proposed a digital signature using a hard algorithmic problem in Braid groups, namely conjugacy problem.

I will then give a survey of some other suggested group-based cryptosystems that could be claimed as post-quantum cryptosystems.**HARK the SHARK: Realized Volatility Modelling with Measurement Errors and Nonlinear Dependencies**

Giuseppe Buccheri, Scuola Normale Superiore Pisa

martedì 6 marzo 2018 alle ore 12:15, Aula seminari terzo piano**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 MILANOABSTRACTI will review recent results on the analysis of graphene via variational methods. The setting is that of Molecular Mechanics: carbon atoms are identified with their nuclear positions and their bonds are described via classical two- and three-body interactions. I will discuss the crystallization problem in both two and three dimensions, the mechanics of the (planar) crystal under tension, the rolling-up of free graphene patches, and the emergence of ripples in suspended samples.

Contact: francesco.bonaldi@polimi.it

**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**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 9ABSTRACTIn Hilbert or Banach spaces $X$ endowed with a good probability measure $\mu$ there are a few “natural” definitions of Sobolev spaces and of spaces of bounded variation functions. The available theory deals mainly with Gaussian measures and Sobolev and BV functions defined in the whole $X$, while the study and Sobolev and BV spaces in domains, and/or with respect to non Gaussian measures, is largely to be developed.

As in finite dimension, Sobolev and BV functions are tools for the study of different problems, in particular for PDEs with infinitely many variables, arising in mathematical physics in the modeling of systems with an

infinite number of degrees of freedom, and in stochastic PDEs through Kolmogorov equations.

In this talk I will describe some of the main features and open problems concerning such function spaces.

**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 MILANOABSTRACTThe numerical simulation of physiological and biomechanics processes allows for a better understanding of many internal mechanism of the human body. For example stresses in joints or the activation sequence of the human heart can be computed “in silico”, thus providing the possibility to develop new therapies or to assist physician in diagnosis and therapy. In order to get close to realistic medical applications, or even to a clinical setting, several difficulties have to be addressed. These contain the efficient simulation of coupled and non-linear partial differential equations, the choice of the appropriate models, and, last but not least, the personalization of the simulation by means of, e.g., parameter fitting or uncertainty quantification. In this talk, we give an overview in numerical techniques in biomechanics and cardiology, including contact problems, the electro-mechanical activation of the human heart, and fluid-structure interaction in heart valves.

Contact: christian.vergara@polimi.it**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 $Q(x)$.