Dipartimento di Matematica – Politecnico di Milano

Prossimi Seminari

Optimal Strategy for a Fund Manager with Option Compensation
Marco Nicolosi, Università degli Studi di Perugia
martedì 30 maggio 2017 alle ore 12:30, Aula Seminari del Terzo Piano
Leggere i dati per progettare le politiche pubbliche per il nuovo millennio: una sfida (im)possibile
Giovanni Azzone – Piercesare Secchi, Politecnico di Milano
mercoledì 31 maggio 2017 alle ore 12:15, Campus Leonardo, via Bonardi 9, aula De Donato
Astronome del passato – Una, nessuna o centomila?
Gabriella Bernardi, Giornalista scientifico
mercoledì 7 giugno 2017 alle ore 12:15, Campus Leonardo, via Bonardi 9, Edificio 14 (Nave), aula B21
Dynamical inverse problems in glucose metabolism of cancer
Michele Piana, Università di Genova, Dipartimento di Matematica
giovedì 15 giugno 2017 alle ore 14:00, Aula Consiglio, VII piano – Dipartimento di Matematica, Politecnico di Milano – Edificio 14
ABSTRACT

ABSTRACT

Glucose metabolism in cancer can be mapped by using positron emission tomography (PET). however, PET data interpration requires the use of regularization techniques for both reconstructing functional images of tissue proliferation and detemining the kinetic parameters that explain the effectivenes of information flow between functional compartments. this talk will illustrate a mathematical model for glucose physiology in healthy and cancerous tissues and how such model can be numerically reduced in order to provide quantitative information on glucose pato-physiology
Imaging the brain microstructure with diffusion-weighted MRI
Maxime Taquet, University of Louvain and Harvard Medical School
lunedì 26 giugno 2017 alle ore 14:00, Aula Consiglio, VII piano – Dipartimento di Matematica, Politecnico di Milano – Edificio 14
ABSTRACT

ABSTRACT

The brain microstructure is the complex organization of axons, neurons and other cells that support the neural functions. Its mapping at the whole-brain level holds promise to the identification and characterization of neurological and psychiatric disorders as well as the assessment of response to treatment. Diffusion-weighted imaging has been at the forefront of developments of brain microstructure imaging. It is based on the recording of movements of pools of water molecules as they hit the cellular barriers in the brain. In this talk, I will provide a gentle introduction to DWI and microstructure imaging, present some recent developments and outline exciting challenges that the field is currently facing.
Dynamical low rank approximation of random time dependent PDEs
Fabio Nobile, Mathematics Institute, CSQI, Ecole Polytechnique Fédérale de Lausanne, Switzerland
giovedì 29 giugno 2017 alle ore 14:00, Aula Consiglio, VII piano – Dipartimento di Matematica, Politecnico di Milano – Edificio 14
ABSTRACT

ABSTRACT

Partial differential equations with random coefficients and input data (random PDEs in short) arise in many applications in which the data of the PDE need to be described in terms of random variables/fields due either to a lack of knowledge of the system or to its inherent variability. The numerical approximation of statistics of the solution poses several challenges when the number of random parameters is large and/or the parameter-to-solution map is complex, and effective surrogate or reduced models are of great need in this context.
In this talk we consider time dependent PDEs with few random parameters and seek for an approximate solution in separable form that can be written at each time instant as a linear combination of linearly independent spatial functions multiplied by linearly independent random variables (low rank approximation) in the spirit of a truncated Karhunen-Loève expansion. Since the optimal deterministic and stochastic modes can significantly change over time, we consider here a dynamical approach where those modes are computed on the fly as solutions of suitable evolution equations. From a geometrical point of view, this corresponds to constraining the original dynamics to the manifold of fixed rank functions, i.e. functions that can be written in separable form with a fixed number of terms. Equivalently, the original equations are projected onto the tangent space to the manifold of fixed rank functions along the approximate trajectory, similarly to the Dirac-Frenkel variational principle in quantum mechanics.
We discuss the construction of the method as well as practical numerical aspects for several time dependent PDEs with random parameters, including the heat equation with a random diffusion coefficient; the incompressible Navier-Stokes equations with random Dirichlet boundary conditions; the wave equation with random wave speed. In the latter case, we propose a dynamical low rank approximation that preserves the symplectic structure of the equations.
Numerical simulations of non-ideal compressible-fluid flows
Alberto Guardone, Politecnico di Milano, Dipartimento di Scienze e Tecnologie Aerospaziali
giovedì 6 luglio 2017 alle ore 14:00, Aula Consiglio, VII piano – Dipartimento di Matematica, Politecnico di Milano – Edificio 14
ABSTRACT

ABSTRACT

In the close proximity of the liquid-vapour saturation curve and critical point, well-known thermodynamic phenomena including large compressibility and critical point effects results in very unusual fluid dynamics features, including non-ideal or rarefaction shock waves, mixed and split waves. This unconventional behaviour, which cannot occur in the ideal flow of dilute gases, is referred to as Non-Ideal Compressible-Fluid Dynamics or NICFD. The focus of this short lecture is to review the theoretical background of NICFD and to discuss the impact of highly non-ideal conditions on the design and properties of numerical schemes for compressible flows. Exemplary flow fields will be presented and compared to available experimental data from the Test-Rig for Organic VApours (TROVA) of Politecnico di Milano, a unique facility in which supersonic flows in non-ideal conditions can be measured and observed. The present results are obtained within the framework of the ERC Consolidator Grant NSHOCK, of which the presenter is the PI.
Multivariate Splines and Their Applications
Ming-Jun Lai, Dept. of Math. University of Georgia, Athens, GA, USA
giovedì 20 luglio 2017 alle ore 14:00, Aula Consiglio, VII piano – Dipartimento di Matematica, Politecnico di Milano – Edificio 14
ABSTRACT

ABSTRACT

Multivariate splines are piecewise polynomial or rational functions over a collection of polygons. We shall explain some approximation properties of these splines and construction of locally supported basis functions. Then I will explain how to use them for numerical solution of linear and nonlinear partial differential equations and data fitting for statistical analysis. Our approach is based on barycentric coordinates (BB form) and generalized barycentric coordinates (GBC). The smoothness conditions, boundary conditions or interpolatory conditions will be set up as linear constraints when we minimize energy functional associated with the PDE to be solved or data to be fitted. Our approach enables us to use higher order polynomials and the smoothness higher than continuity easily. Several numerical examples of PDE and data fitting will be shown.
SPECTRAL THEORY, SUM RULES AND LARGE DEVIATIONS
Barry Simon, California Institute of Technology
lunedì 30 ottobre 2017 alle ore 16:30, Aula Chisini, via Saldini 50
RANDOMNESS IN PARTIAL DIFFERENTIAL EQUATIONS
Felix Otto, Max Plank Institute, Leipzig
lunedì 20 novembre 2017 alle ore 16:30, Aula Chisini, via Saldini 50

Seminari Matematici Politecnico di Milano

Seminari Matematici Milano e dintorni

Archivio Seminari

A posteriori error analysis and adaptive schemes for the wave equation
Omar Lakkis, Free University of Bolzano-Bozen, Faculty of Computer Science and University of Sussex, GB
giovedì 25 maggio 2017 alle ore 14:00, Aula Consiglio, VII piano – Dipartimento di Matematica, Politecnico di Milano – Edificio 14
ABSTRACT
Aposteriori error estimates provide a rigorous foundation for the derivation of efficient adaptive algorithms for the approximation of solutions of partial differential equations (PDEs). While the literature is rich with results for the approximation of elliptic and parabolic PDEs, it is much less developed for the hyperbolic equations such as the acoustic or elastic wave equations. In this talk, I will review some of the “standard” aposteriori results for the scalar linear wave equation, including those of [1] and [2], and present recent improvements and further developments to lower order Sobolev norms based on Baker’s Trick [3] for backward Euler schemes. Subsequent focus will be given to practically relevant methods such as Verlet, Cosine, or Newmark methods, a popular example of which is the Leap-frog method [4].
Notes: This is based on joint work with E.H. Georgoulis, C. Makridakis and J.M. Virtanen.
References:
[1] W. Bangerth and R. Rannacher, J. Comput. Acoust. 9(2):575–591, 2001.
[2] C. Bernardi and E. Süli, Math. Models Methods Appl. Sci. 15(2):199–225, 2005.
[3] E. H. Georgoulis, O. Lakkis, and C. Makridakis. IMA J. Numer. Anal., 33(4):1245–1264, 2013, http://arxiv.org/abs/1003.3641
[4] E. H. Georgoulis, O. Lakkis, C. Makridakis, and J. M. Virtanen. SIAM J. Numer. Anal., 54(1), 2016, http://arxiv.org/abs/1411.7572
ABSTRACT
The isoperimetric problem
Frank Morgan, Williams College
giovedì 25 maggio 2017 alle ore 16:30, Aula Chisini, via Saldini 50
A probabilistic view of the inelastic Boltzmann equation and generalized Kac equations
Federico Bassetti, Dipartimento di Matematica, Università degli Studi di Pavia
giovedì 25 maggio 2017 alle ore 15:15 precise, Sala Maestrale, Tender, piano -1
ABSTRACT
In this talk we present an overview of some results obtained on a class
of measure-valued nonlinear kinetic-type equations. We shall show how
suitable probabilistic techniques, essentially related to central limit
theorems and fixed point equations for distributions, can be fruitfully
used to study these equations. In the first part of the talk, we shall
briefly discuss existence, shape and dynamical stability of equilibria
for the class of one dimensional
generalized Kac equations, whose collisional operator is expressed in
term of a smoothing transformation.
This class of equations includes the well-known Kac model as well its
generalisation to inelastic collisions and also various models used in
econophysic.
In the second part of the talk we will show how the previous results
(partially) extend to the multidimensional homogeneous inelastic
Boltzmann equation.

The talk is based on some joint works with L. Ladelli, D. Matthes, E.
Perversi, E. Regazzini, and G. Toscani.
ABSTRACT
Iannis Xenakis: architetto della luce e del suono
Alessandra Capanna, Università “La Sapienza” ? Roma
mercoledì 24 maggio 2017 alle ore 12:15, Campus Leonardo, via Bonardi 9, Edificio 14 (Nave), aula B21
Transference results from the $L^p$ continuity of operators in the Jacobi case to the $L^p$ continuity of operators in the Hermite and Laguerre case
Wilfredo Urbina, Roosevelt University – Chicago USA
mercoledì 24 maggio 2017 alle ore 13:15, Aula seminari 3° piano
ABSTRACT
Using the well known asymptotic relations between Jacobi polynomials and Hermite and Laguerre polynomials we develop a transference method to obtain the $L^p$-continuity of the Gaussian-Riesz transform and the $L^p$-continuity of the Laguerre-Riesz transform from the $L^p$-continuity of the Jacobi-Riesz transform, in dimension one as well as the $L^p$-continuity of the Gaussian-Riesz transform and the $L^p$-continuity of the Laguerre-Riesz transform from the $L^p$-continuity of the Jacobi-Riesz transform. The case of the corresponding Littlewood-Paley g-functions will also be discussed.
ABSTRACT
Copula Based Multivariate Semi-Markov Models with Applications in High-Frequency Finance
Filippo Petroni, Università di Cagliari
martedì 23 maggio 2017 alle ore 14:00, Aula Seminari del Sesto Piano
Mathematical modeling in physiology and medicine: neurological diseases
Eleuterio Toro, Laboratory of Applied Mathematics, DICAM, University of Trento, Italy
giovedì 18 maggio 2017 alle ore 14:00, Aula Consiglio, VII piano – Dipartimento di Matematica, Politecnico di Milano – Edificio 14
ABSTRACT
There is increasing evidence of the involvement of the dynamics of fluid compartments of the central nervous system (CNS) in the pathophysiology of neurodegenerative diseases.
Supportive recent advances in human physiology include the discovery of a meningeal lymphatic system. A feasible multidisciplinary holistic approach to understand the basic mechanisms at work is offered by mathematical modelling. In this talk I first give a brief review of some neurological diseases thought to be associated to malfunctions of CNS fluid compartments, such as Multiple Sclerosis, Menieres Disease, Idiopathic Parkinsons Disease, Alzheimers Disease and Idiopathic Intracranial Hypertension. I then describe a global, closed loop mathematical model for the entire human circulation coupled to the dynamics of cerebrospinal fluid (CSF) and brain dynamics. Sample computations on the effect of extracranial venous strictures on CNS haemodynamics and CSF dynamics are presented. Intracranial venous hypertension and disturbed CSF dynamics are predicted. These computational results support recent medical hypotheses and may help to unravel some of the underlying mechanisms of some of these diseases, paving the way to treatment strategies. I then point out some of the limitations of our present mathematical model and describe current work aimed at enhancing it, to include the peripheral as well as the newly discovered brain lymphatic system. Some unresolved mathematical and numerical challenges are briefly described.
ABSTRACT
Oltre il nostro Sistema Solare: alla ricerca di un’altra Terra
Barbara Negri , ASI Agenzia Spaziale Italiana
mercoledì 17 maggio 2017 alle ore 12:15, Campus Leonardo, via Bonardi 9, Edificio 14 (Nave), aula B21