25 Maggio, 2017 14:00

MOX Colloquia

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

Aula Consiglio, VII piano - Dipartimento di Matematica, Politecnico di Milano - Edificio 14

abstract

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, arxiv.org/abs/1003.3641
[4] E. H. Georgoulis, O. Lakkis, C. Makridakis, and J. M. Virtanen. SIAM J. Numer. Anal., 54(1), 2016, arxiv.org/abs/1411.7572

I have a PhD in Applied Mathematics and Scientific Computing from the University of Maryland (2002). Then, I have worked as a postdoc at the Università di Milano (2002), the University of Crete and FORTH Heraklion Crete (2003-2004). I have joined the University of Sussex, as a permanent lecturer in (2004-2010), and senior lecturer (2010-2016), currently visiting senior lecturer. In 2016, I have moved my main affiliation to the Free University of Bolzano, where I work at the Faculty of Computer Science. I have visited IPAM at UCLA, California (2002), Hausdorff Institute for Mathematics, Bonn (2008), Basque Center for Applied Mathematics, Bilbao (2011), and ACMAC, Heraklion (2012).

25 Maggio, 2017 16:30

Lezioni Leonardesche

The isoperimetric problem

Frank Morgan, Williams College

Aula Chisini, via Saldini 50

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, arxiv.org/abs/1003.3641
[4] E. H. Georgoulis, O. Lakkis, C. Makridakis, and J. M. Virtanen. SIAM J. Numer. Anal., 54(1), 2016, arxiv.org/abs/1411.7572

I have a PhD in Applied Mathematics and Scientific Computing from the University of Maryland (2002). Then, I have worked as a postdoc at the Università di Milano (2002), the University of Crete and FORTH Heraklion Crete (2003-2004). I have joined the University of Sussex, as a permanent lecturer in (2004-2010), and senior lecturer (2010-2016), currently visiting senior lecturer. In 2016, I have moved my main affiliation to the Free University of Bolzano, where I work at the Faculty of Computer Science. I have visited IPAM at UCLA, California (2002), Hausdorff Institute for Mathematics, Bonn (2008), Basque Center for Applied Mathematics, Bilbao (2011), and ACMAC, Heraklion (2012).

25 Maggio, 2017 15:15 in punto

Sezione di Probabilità e Statistica Matematica

A probabilistic view of the inelastic Boltzmann equation and generalized Kac equations

Federico Bassetti, Dipartimento di Matematica, Università degli Studi di Pavia

Sala Maestrale, Tender, piano -1

abstract

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.

I have a PhD in Applied Mathematics and Scientific Computing from the University of Maryland (2002). Then, I have worked as a postdoc at the Università di Milano (2002), the University of Crete and FORTH Heraklion Crete (2003-2004). I have joined the University of Sussex, as a permanent lecturer in (2004-2010), and senior lecturer (2010-2016), currently visiting senior lecturer. In 2016, I have moved my main affiliation to the Free University of Bolzano, where I work at the Faculty of Computer Science. I have visited IPAM at UCLA, California (2002), Hausdorff Institute for Mathematics, Bonn (2008), Basque Center for Applied Mathematics, Bilbao (2011), and ACMAC, Heraklion (2012).

24 Maggio, 2017 12:15

Seminari di Cultura Matematica

Iannis Xenakis: architetto della luce e del suono

Alessandra Capanna, Università La Sapienza Roma

Campus Leonardo, via Bonardi 9, Edificio 14 (Nave), aula B21

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.

I have a PhD in Applied Mathematics and Scientific Computing from the University of Maryland (2002). Then, I have worked as a postdoc at the Università di Milano (2002), the University of Crete and FORTH Heraklion Crete (2003-2004). I have joined the University of Sussex, as a permanent lecturer in (2004-2010), and senior lecturer (2010-2016), currently visiting senior lecturer. In 2016, I have moved my main affiliation to the Free University of Bolzano, where I work at the Faculty of Computer Science. I have visited IPAM at UCLA, California (2002), Hausdorff Institute for Mathematics, Bonn (2008), Basque Center for Applied Mathematics, Bilbao (2011), and ACMAC, Heraklion (2012).

24 Maggio, 2017 13:15

Sezione di Analisi

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

Aula seminari 3° piano

abstract

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.

I have a PhD in Applied Mathematics and Scientific Computing from the University of Maryland (2002). Then, I have worked as a postdoc at the Università di Milano (2002), the University of Crete and FORTH Heraklion Crete (2003-2004). I have joined the University of Sussex, as a permanent lecturer in (2004-2010), and senior lecturer (2010-2016), currently visiting senior lecturer. In 2016, I have moved my main affiliation to the Free University of Bolzano, where I work at the Faculty of Computer Science. I have visited IPAM at UCLA, California (2002), Hausdorff Institute for Mathematics, Bonn (2008), Basque Center for Applied Mathematics, Bilbao (2011), and ACMAC, Heraklion (2012).

23 Maggio, 2017 14:00

Sezione di Finanza Quantitativa

Copula Based Multivariate Semi-Markov Models with Applications in High-Frequency Finance

Filippo Petroni, Università di Cagliari

Aula Seminari del Sesto Piano

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.

I have a PhD in Applied Mathematics and Scientific Computing from the University of Maryland (2002). Then, I have worked as a postdoc at the Università di Milano (2002), the University of Crete and FORTH Heraklion Crete (2003-2004). I have joined the University of Sussex, as a permanent lecturer in (2004-2010), and senior lecturer (2010-2016), currently visiting senior lecturer. In 2016, I have moved my main affiliation to the Free University of Bolzano, where I work at the Faculty of Computer Science. I have visited IPAM at UCLA, California (2002), Hausdorff Institute for Mathematics, Bonn (2008), Basque Center for Applied Mathematics, Bilbao (2011), and ACMAC, Heraklion (2012).

18 Maggio, 2017 14:00

MOX Colloquia

Mathematical modeling in physiology and medicine: neurological diseases

Eleuterio Toro, Laboratory of Applied Mathematics, DICAM, University of Trento, Italy

Aula Consiglio, VII piano - Dipartimento di Matematica, Politecnico di Milano - Edificio 14

abstract

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.

The research of prof Toro has for many years focused on the construction of computational methods for solving partial differential equations, with particular emphasis on hyperbolic balance laws. Currently it is focused on the study of neurodegenerative diseases. He is authors of several books on numerical methods for hyperbolic problems and received several honours, such as the "Officer of the Most Excellent Order of the British Empire" from the Queen

17 Maggio, 2017 12:15

Seminari di Cultura Matematica

Oltre il nostro Sistema Solare: alla ricerca di un'altra Terra

Barbara Negri, ASI Agenzia Spaziale Italiana

Campus Leonardo, via Bonardi 9, Edificio 14 (Nave), aula B21

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.

The research of prof Toro has for many years focused on the construction of computational methods for solving partial differential equations, with particular emphasis on hyperbolic balance laws. Currently it is focused on the study of neurodegenerative diseases. He is authors of several books on numerical methods for hyperbolic problems and received several honours, such as the "Officer of the Most Excellent Order of the British Empire" from the Queen

16 Maggio, 2017 10:30

Seminario Matematico e Fisico di Milano

DYNAMICAL SYSTEMS AND GEOMETRY OF CAUCHY-RIEMANN MANIFOLDS

Laurent Stolovitch, Universite' de Nice Sophia-Antipolis

Sala di rappresentanza, Dipartimento di Matematica, Università degli Studi, Via C. Saldini 50

abstract

abstract

In this talk, I show how (local) dynamical systems can be used in order to understand the geometry of real submanifolds in the complex euclidean space

The research of prof Toro has for many years focused on the construction of computational methods for solving partial differential equations, with particular emphasis on hyperbolic balance laws. Currently it is focused on the study of neurodegenerative diseases. He is authors of several books on numerical methods for hyperbolic problems and received several honours, such as the "Officer of the Most Excellent Order of the British Empire" from the Queen

11 Maggio, 2017 14:15

Sezione di Analisi

Sublinear elliptic problems with a Hardy potential

Catherine Bandle, University of Basel

Aula Consiglio 7° piano

abstract

abstract

We discuss the existence and the boundary behavior of positive solutions of an elliptic equation with a Hardy potential and a sublinear nonlinearity. This problem has two particular features: the Hardy potential is singular at the boundary and the unique continuation property doesn’t hold. The Hardy potential forces the solutions either to vanish or to blow up at the boundary. The picture of the radial solutions in balls and annuli is fairly complete. At the end we present results for general domains and point out some open problems.

The research of prof Toro has for many years focused on the construction of computational methods for solving partial differential equations, with particular emphasis on hyperbolic balance laws. Currently it is focused on the study of neurodegenerative diseases. He is authors of several books on numerical methods for hyperbolic problems and received several honours, such as the "Officer of the Most Excellent Order of the British Empire" from the Queen