20 Maggio, 2009 12:15

Seminari di Cultura Matematica

Matematica, astronomia e architettura a Giza, Egitto

Giulio Magli, Politecnico di Milano

Aula B 2.1, Via Bonardi 9

20 Maggio, 2009 16:15

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

On a semiconductor drift-diffusion-Poisson model in R3

Wu Hao, Fudan University Shanghai e WIAS Berlin

Sala Seminari Fausto Saleri , VI piano

abstract

abstract

We study a time-dependent as well as a stationary
drift-diffusion-Poisson system for semiconductors. Global existence
and uniqueness of weak solution of the time-dependent problem are
proven and we also prove the existence and uniqueness of the steady
state. Finally, we discuss the large time asymptotics of the
time-dependent problem. This is a joint work with Prof. P. Markowich
and Prof. S. Zheng.

20 Maggio, 2009 17:15

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Tame Functions and Variational Analysis

Alexander Ioffe, Department of Mathematics, The Technion, Haifa

Aula seminari Fausto Saleri, 6 piano

abstract

abstract

All non-trivial theorems of local variational analysis applied to generic
non-differential functions (e.g. optimization problems with generic
Lipschitz data) produce not very informative, often just trivial
results. Fortunately, functions that usually appear in applications
have some special structures (e.g. polyhedral, linear-quadratic, spline
etc.). Typically such structures are particular cases of semi-algebraic
(or more generally, tame) structures. The latter turn out to be perfectly
compatible with basic constructions of local variational analysis which
excludes any possibility for the mentioned unpleasant phenomena to happen.
Moreover, in this case a number of powerful results can be proved that
are not otherwise valid.
The latter statements will be clarified in the talk, both in general terms
and for some important classes of problems, including standard problems of
mathematical programming, gradient dynamical systems and optimal control
of state-linear systems.

18 Maggio, 2009 14:00

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

The multigrid strategy for solving elliptic optimal control problems

Alfio Borzi, Universita degli studi del Sannio

Aula F. saleri VI Piano Dipartimento di Matematica

abstract

abstract

Recent efforts in the development and analysis of multigrid methods for solving elliptic PDE-based control problems are illustrated.
These problems consist of an elliptic model including an optimization mechanism and an objective of the control. The solution to these problems is characterized by an optimality system that also provides gradient information for the related minimization procedure.

It is shown that fast and robust solution schemes for elliptic optimal control problems are obtained based on the multigrid strategy.
On the one hand, direct one-shot multigrid methods can be implemented that solve the optimality system within the hierarchy of grid levels. The essential component of this approach is the formulation of appropriate smoothers.

On the other hand, it is possible to formulate optimization schemes where the multigrid method defines the outer solver and the inner solver is given by a classical optimization procedure. This is an emerging research field leading to reinterpreting multigrid algorithms from an optimization point of view.

14 Maggio, 2009 15:00

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Components of atmospheric models used for numerical weather prediction over days, months, seasons and decades

Adrian Tompkins, International Center of Theoretical Physics, Trieste

Aula F. Saleri VI Piano Mox - Dipartimento di Matematica -

abstract

abstract

Numerical weather prediction models are the tools used to provide the daily short-range weather forecasts issued to the public in the media.
However, most numerical weather centres run a range of models covering timescales from days to many months. These models may be global in
extent, or may only cover a local region. Due to computing resourcelimitations, even regional-scale models solve the equations of motions of a grid of points too coarse to resolve all processes and scales of motions that are of relevance. These have to be represented by
simplified models, or parametrizations. One example is convective and cloud processes which will be discussed. This talks will give an
overview of the components of models used from daily to seasonal tiemscales and beyond, highlighting some differences and similarities.
The systems of the European Centre for Medium Range Weather Forecasts will be used as an example. Active areas and outstanding questions
concerning future NWP model development will be raised.

14 Maggio, 2009 14:00

Sezione di Geometria, Algebra e loro applicazioni

A short history of algebraic statistics

Eva Riccomagno, Universita degli Studi di Genova

Aula interna 7 piano

abstract

abstract

Polynomials and ratios of polynomials appear in statistics and probability under various forms, in model representations as well as in inferential procedures. Algebraic geometry studies (ratios of) polynomials and the zeros set of systems of polynomial equations. Algebraic statistics uses techniques from (real) algebraic geometry, and commutative algebra, geometric combinatorics, ... to gain insight into the structure and properties of statistical models and to advise in model analysis. This, in turn, may prompt research in algebraic geometry.

(Published in Metrika 2009 69:397-418)

13 Maggio, 2009 12:15

Seminari di Cultura Matematica

Il vetro e le scienze nel mondo antico

Marco Beretta, Università di Bologna

Aula B 2.1, Via Bonardi 9

Polynomials and ratios of polynomials appear in statistics and probability under various forms, in model representations as well as in inferential procedures. Algebraic geometry studies (ratios of) polynomials and the zeros set of systems of polynomial equations. Algebraic statistics uses techniques from (real) algebraic geometry, and commutative algebra, geometric combinatorics, ... to gain insight into the structure and properties of statistical models and to advise in model analysis. This, in turn, may prompt research in algebraic geometry.

(Published in Metrika 2009 69:397-418)

12 Maggio, 2009 14:00

Sezione di Geometria, Algebra e loro applicazioni

Some combinatorics related to central binomial coefficients: Grand-Dyck paths, coloured noncrossing partitions and signed pattern avoiding permutations

Luca Ferrari, Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze

Aula seminari III piano

abstract

abstract

Vengono studiate proprietà enumerative e d ordine di alcune strutture combinatorie contate dai coefficienti binomiali centrali. In particolare, vengono determinate nuove biiezioni fra cammini di Grand-Dyck e specifiche classi di permutazioni colorate a motivo escluso e si dimostra che i reticoli dei cammini di Grand-Dyck di lunghezza fissata sono isomorfi a determinati sottoinsiemi parzialmente ordinati dell ordine di Bruhat sulle permutazioni colorate che escludono specifici motivi, anch essi colorati.

8 Maggio, 2009 11:00

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

About existence for optimal 1-rectifiable transports

Guy BOUCHITTE, Université de Toulon

Aula seminari Fausto Saleri, 6 piano

Vengono studiate proprietà enumerative e d ordine di alcune strutture combinatorie contate dai coefficienti binomiali centrali. In particolare, vengono determinate nuove biiezioni fra cammini di Grand-Dyck e specifiche classi di permutazioni colorate a motivo escluso e si dimostra che i reticoli dei cammini di Grand-Dyck di lunghezza fissata sono isomorfi a determinati sottoinsiemi parzialmente ordinati dell ordine di Bruhat sulle permutazioni colorate che escludono specifici motivi, anch essi colorati.

6 Maggio, 2009 15:00

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Continuation of branch points of algebraic and boundary-value problems

Fabio Dercole, Dipartimento di Elettronica e Informazione Politecnico di Milano

Aula F. Saleri VI Piano Mox - Dipartimento di Matematica -

abstract

abstract

The numerical continuation of simple branch points of algebraic and boundary-value problems is described in detail. Simple branch points are points in the continuation space where two solution branches intersect transversally. Detection and accurate location of branch points along the continuation of a solution branch and switching to the continuation of the other branch are implemented in most software packages, but branch point continuation has not been fully supported.
In particular, generic problems, where branch point continuation is performed in two extra parameters, must be distinguished from non-generic cases, where one extra parameter is typically involved due to problem-specific symmetries. This talk presents the extended algebraic and boundary-value problems which define branch point continuation, discusses their initialization at branch point detection and the symmetry breaking technique used to automatically handle non-generic cases, and describes the implementation in the software package Auto. Several examples, including generic and non-generic algebraic problems, generic and non-generic periodic boundary-value problems, and a non-generic non-periodic boundary-value problem, are also presented.