Direttore Vicario: Prof. Gabriele Grillo
Responsabile Gestionale: Dr.ssa Franca Di Censo

### Seminari

 Selezionare una sezione Tutte Algebra e Informatica Teorica Analisi Analisi Numerica Calcolo delle variazioni Dipartimento FDS Finanza Quantitativa Fisica Matematica Geometria Lezioni Leonardesche Matematica Discreta MOX Probabilità Quantistica Probabilità e Statistica Matematica Seminario Matematico e Fisico Seminari di Cultura Matematica Tomografia e Applicazioni Parola da cercare

### Prossimi Seminari

• A mathematical-physics approach to machine learning
Pierluigi Contucci, Dipartimento di Matematica Università di Bologna
giovedì 30 gennaio 2020 alle ore 14:00, Aula Saleri VI piano
• Modeling and simulation of thermo-poroelastic processes in fractured geothermal reservoirs
Eirik Keilegavlen, Department of Mathematics, University of Bergen, Norway
giovedì 20 febbraio 2020 alle ore 11:30, Aula Saleri - VI piano

### Seminari Passati

• Three body problems in quantum mechanics
Wu-Yi Hsiang, Hong Kong University of Science and Technology (Hong Kong, Cina)
mercoledì 26 maggio 2004 alle ore 17:00, Dipartimento di Matematica - Università degli Studi di Milano - Via Saldini 50 - Milano - Sala di Rappresentanza
ABSTRACT
In this talk, I shall describe the geometric approach to solve the Schrödinger equation for various physically meaningful three body systems such as He, H2+, H-, three bosons in R2 with d-function potential etc. The configuration space of the three body system in R3(resp. R2) (with center of gravity fixed at the origin) is an R6 (resp. R4) equipped with an SO(3) (resp. SO(2)) symmetric kinematic metric, while the potential function U is also SO(3) (resp. SO(2)) invariant. The first step is to fully utilize the SO(3) (resp. SO(2)) symmetry to reduce the Schrödinger equation to an equation solely defined at the level of the orbit space (i.e. R6/SO(3) (resp. R4/SO(2))) equipped with the orbital distance metric. One needs to make effective use of both group representation theory and equivariant differential geometry to achieve such a reduction. The orbit space of a three body system in R3 (resp. R2) equipped with the orbital distance metric is always isometric to the Riemannian cone over S2+ (1/2) (resp. S2(1/2))), namely the Euclidean hemisphere (resp. sphere) of radius 1/2. This remarkable fact (i.e. sphericality) enables us to bring in the spherical harmonics and their generalizations (namely, Jacobi polynomials and monopole harmonics) to greatly simplify the analysis of the angular part of the reduced equation. I will use the simpler case of the boson system to illustrate this step which enables us to further reduce the Schrödinger equation to an ODE solely in the radial direction. Such an ODE can be thoroughly analyzed and I will discuss the physical significance of these solutions so obtained for the three boson system. Bibliography Wu-Yi Hsiang. Kinematic geometry of mass-triangles and reduction of Schr¨odinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters. Proc. Nat. Acad. Sci. U.S.A., 94(17):8936–8938, 1997. Wu-Yi Hsiang. On the kinematic geometry of many body systems. Chinese Ann. Math. Ser. B, 20(1):11–28, 1999. A Chinese summary appears in Chinese Ann. Math. Ser. A 20 (1999), no. 1, 141.
• Sistemi dinamici ed i fondamenti della termodinamica
L. Galgani, Univ. di Milano
venerdì 21 maggio 2004 alle ore 12:30, Aula B.21
• Nonextensive statistical mechanics - Introduction and dynamical foundations
Constantino Tsallis, Centro Brasileiro de Pesquisas Físicas (Rio de Janeiro, Brasile)
venerdì 21 maggio 2004 alle ore 17:00, Dipartimento di Matematica - Università degli Studi di Milano - Via Saldini 50 - Milano - Sala di Rappresentanza
ABSTRACT
"Nonlinear dynamical systems that satisfy hypothesis such as ergodicity and exponentially quick mixing are well known to be adequately studied in terms of the Boltzmann-Gibbs entropy and its corresponding statistical mechanics. These simplifying hypothesis are however NOT satisfied in vast classes of systems such as the so called ""complex systems"", ubiquitously emerging in physics, mathematics, economics, linguistics, chemistry, astrophysics, geophysics, biology, computer networks, engineering and elsewhere. A nonextensive entropy (characterized by an entropic index q, which reproduces the Boltzmann-Gibbs expression for q = 1) and its corresponding statistical mechanics provide an answer for at least part of such anomalous systems. A brief introduction will be given to the subject, followed by a survey on its dynamical foundations, which enable in particular the calculation, from first principles, of the index q associated with specific systems. Recent bibliography: ""Nonextensive Entropy - Interdisciplinary Applications"", M. Gell-Mann and C. Tsallis, eds. (Oxford University Press, New York, 2004) Full bibliography"
• Onde solitarie e campi elettromagnetici
Donato Fortunato, Università di Bari
mercoledì 19 maggio 2004 alle ore 11:30, Dipartimento di Matematica e Applicazioni - Università degli Studi di Milano Bicocca - Via Bicocca degli Arcimboldi, 8 - Aula Dottorato
• Approximation of multi-scale elliptic problems using patches of finite elements
Joel Wagner, iacs-epfl
lunedì 17 maggio 2004 alle ore 14:30, Aula Seminari MOX-6° piano dip di matematica
ABSTRACT
The objective of this seminar is to present a new method to solve numerically
elliptic problems such that a better precision on the solution is needed
in certain regions of the domain wherein the equations
are to be solved (C.R.Acad.Sci.Paris, Ser.I 337 (2003) 679--684).
The approximation of this type of problems with multi-scale data can be approached using
various methods. The technique we present uses multiple levels of not necessarily nested
grids. It is a Schwarz type domain decomposition method with complete overlapping.
The proposed algorithm consists in solving the problem on a domain wherein we consider
patches of elements in the regions where we would like to obtain more accuracy.
Thus we calculate successively corrections to the solution in the patches.
The discretizations of the latter are not necessarily conforming.
The method resembles the Fast Adaptive Composite grid method or possibly
a hierarchical method with a mortar method. However it is of much more flexible use
in comparison to the latter.

The motivation for developing such a method is for example founded in air quality management.
Pollution emission sources, and in particular point source plumes, give
rise to models needing careful examination of the space-scale. Getting an accurate
simulation on large scales is linked to a simulation in subregions around the
pollution sources using finer grids. Such a method can straightforwardly be applied
on boundary layer problems through the use of patches in critical regions.

In this talk we present the algorithm and illustrate its efficiency through a model problem.
We compare the speed of convergence on nested and non-nested, structured and unstructured grids.
A spectral analysis of the iteration operator enables us to give a good estimate of the convergence
rate for given grids. It also leads to a numerical method to evaluate the
constant of the Cauchy-Buniakowski-Schwarz inequality in certain cases of approximation spaces.
Finally we illustrate on several examples our \emph{a priori} estimate for
the convergence in the grid-size.
• Principi variazionali in fisica
H. Kijowski, Warsaw Univ.
venerdì 14 maggio 2004 alle ore 12:30, Aula B.21
• Alcuni risultati sulla distribuzione della varianza di un processo di Dirichlet
dott.ssa ALESSANDRA GUGLIELMI, CNR-IMATI
giovedì 13 maggio 2004 alle ore 16:30, Aula Seminari MOX, VI piano
ABSTRACT
Un problema interessante in ambito bayesiano non parametrico è la determinazione della legge di funzionali di misure di probabilità aleatorie.
In particolare, di recente sono apparsi diversi lavori sulla determinazione della legge esatta di (vettori di) medie di processi di Dirichlet. In questo seminario illustrerò, invece, alcuni risultati sulla distribuzione della varianza V di un processo di Dirichlet P.
Anzitutto, a partire da una certa espressione dei momenti di V, mostrerò l'esistenza di un legame tra la legge della varianza e quella di una funzione della media del processo di Dirichlet P, mettendo in luce alcune delle sue conseguenze. Poi mostrerò l'esistenza di una corrispondenza tra la distribuzione della varianza e il parametro del processo, con massa totale fissata, quando detto parametro varia nella classe delle misure simmetriche.
Nel corso del seminario, saranno discussi alcuni esempi.
Il lavoro su cui si basa il seminario e' stato svolto in collaborazione con Ilenia Epifani (Politecnico di Milano) ed Eugenio Melilli (Universita' Bocconi, Milano).
• Dissecting the Pythagorean proposition
Douglas Rogers, University of Tasmania
mercoledì 12 maggio 2004 alle ore 14:30, CNR, Milano