7 Febbraio, 2018 16:30

Sezione di Analisi

Critical aspects of Choquard type equations

Daniele Cassani, Università degli Studi dell'Insubria

Aula seminari 3° piano

abstract

abstract

We 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).

6 Febbraio, 2018 15:15

Sezione di Analisi

Entropy methods for parabolic and elliptic equations

Jean Dolbeault, Ceremade

Aula seminari 3° piano

abstract

abstract

Entropy methods associated with linear and nonlinear parabolic equations are powerful tools for establishing results of symmetry, unique- ness and optimality in functional inequalities. Optimality cases can be identified by considering asymptotic regimes and appropriate lineariza- tions. Entropy methods raise various issues of regularity and rely on integrations by parts which are not straightforward to justify. On the other hand, these methods give optimal criteria in some fundamental examples. This lecture will be devoted to an overview of the state of the art and list some open questions.

5 Febbraio, 2018 15:00

MOX Seminar

Approximated solution of some integro-differential equations of the Fredholm type

M. Victoria Fernandez Munoz, University of Granada -Spain -

Aula Consiglio VII Piano -edificio 14 Dipartimento di Matematica POLITECNICO DI MILANO

abstract

abstract

Contact: franca.calio@polimi.it

5 Febbraio, 2018 16:00

Seminario Matematico e Fisico di Milano

On the weak maximum principle in unbounded domains

Italo Capuzzo Dolcetta, Università di Roma La Sapienza

Sala di Rappresentanza, Università di Milano, Via C. Saldini 50, Milano

Contact: franca.calio@polimi.it

31 Gennaio, 2018 15:00

Seminari FDS

La matematica computazionale applicata alla medicina: risposte quantitative a diversi problemi clinici

Christian Vergara, Politecnico di Milano

Sala Consiglio VII piano, Dip. di Matematica

abstract

abstract

I modelli matematici permettono di descrivere quantitativamente il comportamento fisiologico e patologico del sistema cardiovascolare, dalla fluido-dinamica del sangue alla sua interazione con le pareti vascolari,
dalla attività elettrica del cuore alla sua interazione con la contrazione cardiaca, giusto per citare qualche esempio.
Al fine di ottenere risultati fruibili dai clinici, metodi numerici e computazionali sono utilizzati, che permettono di risolvere i problemi originari in maniera approssimata tramite l'ausilio di grandi calcolatori.
Ciò permette di studiare delle situazioni patologiche al fine di capire meglio la loro causa e/o sviluppo e in caso di meglio progettare delle soluzioni terapeutiche. In questo contributo verranno riportati degli esempi a riguardo, in particolare la aterosclerosi in carotidi e coronarie, i disturbi elettrici nel ventricolo sinistro, il malfunzionamento delle valvole cardiache.

26 Gennaio, 2018 15:30 in punto

Sezione di Geometria, Algebra e loro applicazioni

On the cone of effective cycles on the symmetric products of a curve

Filippo Viviani, Universita' Roma Tre

Aula seminari del terzo piano

abstract

abstract

I will report on a joint work with F. Bastianelli, A. Kouvidakis and A. F. Lopez in which we study the cone of (pseudo-)effective cycles on symmetric products of a curve. We first prove that the diagonal
cycles span a face of the pseudo-effective cone of cycles in any given dimension. Secondly, we look at the contractibility faces associated to the Abel-Jacobi morphism towards the Jacobian and in many cases
we are able to compute their dimension. The geometry of linear series of a curve (e.g. the classical Brill-Noether theory) will play a special role in our analysis.

18 Gennaio, 2018 14:00

MOX Colloquia

Combining in vitro and in silico approaches towards patient-specific cardiovascular investigations

Gabriele Dubini, Department of Chemistry, Materials and Chemical Engineering G. Natta, Politecnico di Milano

Aula Consiglio VII Piano - Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO

abstract

abstract

This seminar will outline the workflow developed at the Laboratory of Biological Structure Mechanics – LaBS, Politecnico di Milano. (www.labsmech.polimi.it) for the investigation of cardiovascular devices. The combined in vitro and in silico approach will be applied to the study of stenting procedures of peripheral arteries in idealized and patient-specific models as well as to the study of percutaneous aortic valves, where fluid-structure interaction simulations are required. Such examples will demonstrate the extent to which performances of minimally-invasive devices are related to their design, the materials and the applied loads.

contact: christian.vergara@polimi.it

G. Dubini is Full Professor at the Department of Chemistry, Materials and Chemical Engineering G. Natta, Politecnico di Milano. He was the Director of the Laboratory of Biological Structure Mechanics (LaBS) at Politecnico di Milano in 2003-2007. From 2008 to 2012 he was member of the Council of the European Society of Biomechanics (ESB), and the Secretary General from 2010 to 2012. His main research interests are the virtual planning of paediatric cardiac surgery procedures and minimally invasive vascular procedures, the design and characterisation of endovascular and microfluidic devices for biomedical applications

16 Gennaio, 2018 15:15

Sezione di Analisi

Torsional instability in two nonlinear isolated models for suspension bridges

Alessio Falocchi, Politecnico di Milano

Aula seminari 6° piano

abstract

abstract

Many observations throughout history have recorded that torsional instability afflicts suspension bridges. In the scientific community there is not an unanimously accepted explanation about the origin of instability. We present two new dynamical isolated models derived from variational principles and we study two nonlinear hyperbolic partial differential equations, involving the vertical displacement and the torsional rotation of the deck.
In the first model we consider three different nonlinearities to model the hangers slackening mechanisms; in the second one we deal with the nonlinearities due to the geometric configuration of the main cables, supposed deformable, and we prove the existence and uniqueness of a weak solution. We show some numerical experiments, highlighting the torsional instability phenomena with respect to the longitudinal modes excited. Our results suggest that the origin of the instability is hidden in the nonlinear behavior of these structures.

G. Dubini is Full Professor at the Department of Chemistry, Materials and Chemical Engineering G. Natta, Politecnico di Milano. He was the Director of the Laboratory of Biological Structure Mechanics (LaBS) at Politecnico di Milano in 2003-2007. From 2008 to 2012 he was member of the Council of the European Society of Biomechanics (ESB), and the Secretary General from 2010 to 2012. His main research interests are the virtual planning of paediatric cardiac surgery procedures and minimally invasive vascular procedures, the design and characterisation of endovascular and microfluidic devices for biomedical applications

15 Gennaio, 2018 17:00

Seminario Matematico e Fisico di Milano

Variational method for dynamical PET reconstruction

Maïtine Bergounioux, Université d'Orléans

Sala Consiglio, 7 piano, Edificio La Nave, Via Bonardi 9

abstract

abstract

We consider PET (Positron-emission tomography) which a medical imaging technique. We deal with dynamical PET (only static one has a clinical use by now) . I will explain the physical process and set a variational model that takes into account the whole spatio-temporal infomation. Theoretical and numerical results are presented.

G. Dubini is Full Professor at the Department of Chemistry, Materials and Chemical Engineering G. Natta, Politecnico di Milano. He was the Director of the Laboratory of Biological Structure Mechanics (LaBS) at Politecnico di Milano in 2003-2007. From 2008 to 2012 he was member of the Council of the European Society of Biomechanics (ESB), and the Secretary General from 2010 to 2012. His main research interests are the virtual planning of paediatric cardiac surgery procedures and minimally invasive vascular procedures, the design and characterisation of endovascular and microfluidic devices for biomedical applications

12 Gennaio, 2018 15:30 in punto

Sezione di Geometria, Algebra e loro applicazioni

TROPICAL APPROACHES TO BRILL–NOETHER THEORY

Marta Panizzut, TU Berlin

Aula seminari del terzo piano

abstract

abstract

Loosely speaking, tropical geometry aims to transform algebro-geometric problems into combinatorial ones that are hopefully easier to understand. Tropical curves are connected metric graphs, and a theory of linear systems on graphs has been introduced by Baker and Norine in analogy with the one on algebraic curves. Their groundbreaking work has led to the development of a tropical Brill–Noether theory, which provides new combinatorial insights in the study of linear systems on curves. The interplay between the tropical and the classical theory is given by specialization of linear systems from the generic fiber of a 1-parameter family of curves to the dual graph of the special fiber. In this talk, I will begin by introducing the terminology and some of the
main results of this recent theory. Then I will address questions on smooth plane curves and generic smooth curves on P1 × P1 by specializing their linear systems to complete graphs and complete bipartite graphs. This based on joint works with with Filip Cools, Michele D’Adderio and
David Jensen.

G. Dubini is Full Professor at the Department of Chemistry, Materials and Chemical Engineering G. Natta, Politecnico di Milano. He was the Director of the Laboratory of Biological Structure Mechanics (LaBS) at Politecnico di Milano in 2003-2007. From 2008 to 2012 he was member of the Council of the European Society of Biomechanics (ESB), and the Secretary General from 2010 to 2012. His main research interests are the virtual planning of paediatric cardiac surgery procedures and minimally invasive vascular procedures, the design and characterisation of endovascular and microfluidic devices for biomedical applications