Set 212023

Teacher: Prof. Antonio Greco

Language: English

Duration: 8 lectures of 2 hours each (16 hours total)

Timetable: One lecture per week. Details will be specified on the occasion of the first lecture, which will be given on October 20, 2023 at 4 p.m. in room B of the Department of Mathematics and Computer Science

Abstract. The course is an introduction to the problem of determining the shape of solutions to boundary-value problems for second-order partial differential equations, mainly of elliptic type, occasionally parabolic.

1. Review of the weak maximum principle, the strong maximum principle, and the Hopf lemma.
2. Some motivations for Geometric Analysis and some characteristic results: the soap bubble theorem (Aleksandrov’s theorem), Serrin’s overdetermined problem, the Gidas-Ni-Nirenberg symmetry result.
3. Convexity of solutions to the Dirichlet problem. Quasiconvexity.
4. The Morse index of a solution and its role in Geometric Analysis. Work in progress.


Gidas, B.; Ni, Wei-Ming; Nirenberg, L.
Symmetry and related properties via the maximum principle.
Commun. Math. Phys. 68, 209-243 (1979).

Berestycki, H.; Nirenberg, L.
On the method of moving planes and the sliding method.
Bol. Soc. Bras. Mat., Nova Sér. 22, No. 1, 1-37 (1991).

Fraenkel, L. E.
An introduction to maximum principles and symmetry in elliptic problems.
Cambridge University Press. x, 340 p. (2011).

Protter, Murray H.; Weinberger, Hans F.
Maximum principles in differential equations.
Prentice-Hall, Inc. X, 261 p. (1967).

Serrin, James
A symmetry problem in potential theory.
Arch. Ration. Mech. Anal. 43, 304-318 (1971).

Sperb, Rene P.
Maximum principles and their applications.
Academic Press. IX, 224 p. (1981).

Credits: 3,2 CFR (with final talk)

Giu 232023

During the period April 26 – May 16, 2023, Prof. Vasile Staicu
(University of Aveiro) has given a PhD course while visiting the
Department of Mathematics and Computer Sciences within the Visiting
Professor Program of INdAM.

The aim of this course is to present some methods and tools used in
the study of nonlinear boundary value problems involving multivalued
maps and nonsmooth functions and illustrate those methods with some
recent results concerning existence and multiplicity of solutions.

We start by introducing some notions of multivalued analysis:
multivalued maps and their continuity. Then we introduce some elements
of nonsmooth analysis that we use to develop nonsmooth critical point
theory succeeded in extending a big part of the smooth theory to
nonsmooth functionals: the main tool in the variational method for
solving boundary value problems, which consists of trying to find
solutions for a given boundary value problem by looking for stationary
points of a real functional defined on a space of functions in which
the solution of the boundary value problem is assumed to lie. 

Degree theory is a basic tool of nonlinear analysis and produces
powerful existence and multiplicity results for nonlinear boundary
value problems. We present a generalization of Brouwer degree theory
to multivalued perturbations of monotone type maps, developed in a
joint paper with Aizicovici and Papageorgiou (Mem. Amer. Math. Soc.,
196, 2008). Then we consider a nonlinear Dirichlet problem with
nonsmooth potential (hemivariational inequality) and use variational
method to prove two constant sign solutions (one positive and another
negative) and then by using degree theoretical approach we prove the
existence of a third one, nontrivial solution, distinct from the
previous two.

We present several existence and multiplicity results, with sign
information for the solutions of nonlinear boundary value problems
driven by the Laplacian, the p-Laplacian and then try to extend such
results to nonlinear boundary value problems driven by fractional
order differential operators and to nonlocal pseudo-differential
inclusions, possibly including obstacles or constraints. It is
reasonable to expect that the pairing of nonlocal diffusion operators
and set-valued reaction will provide a more realistic model for
applications to such problems as quantum mechanics, image restoration,
and financial mathematics, which typically present a high degree of
uncertainty, rather than elliptic equations with smooth, single-valued

Lecture notes will be provided and open questions will be considered
and analyzed with the Ph. D. students.

Schedule: 27/4 11-13 28/4 9-11 2/5 11-13 5/5 9-11 9/5 11-13 11/5
11-13 12/5 9-11 16/5 11-13 (room F)

Staicu Lecture Notes

 Scritto da in 23 Giugno 2023  Senza categoria  Commenti disabilitati su PhD course: Boundary value problems with nonsmooth and multivalued terms
Gen 042023

Seminario dottorale:

Matrix functions: Computation and application to Complex Networks analysis

Dott. Caterina Fenu

Dipartimento di Matematica e Informatica
Università degli Studi di Cagliari

Il corso si svolgerà in Aula II da lunedì 16/01/23 a venerdì 20/01/23 dalle 10 alle 12 e contemporaneamente sul Team Matrix functions: 

Computation and application to Complex Networks analysis (il codice per unirsi al Team è: okf8wgi).

The aim of the course is to introduce basic concepts related to the computation
of matrix functions and their use in the analysis of complex networks. Half of the
course will be dedicated to the implementation of some algorithms by using the
MATLAB software.
Outline of the course
• Linear algebra: eigenvalue decomposition, Jordan decomposition, singular
value decompo- sition;
• Introduction to matrix functions and bilinear/quadratic forms: orthogonal
polynomials, Lanczos algorithms, quadrature formulas;
• Introduction to complex networks theory: graphs, centrality/communicability
indices, network indices;
• Use of the MATLAB software.
The oral exam will consist of a discussion of a research paper concerning the topics
of the course.
1. G. H. Golub and G. Meurant, Matrices, Moments and Quadrature with Appli-
cations, Princeton University Press, Princeton, 2010.
2. N. J. Higham, Functions of matrices: theory and computation, SIAM, 2008.
3. W. Gautschi, Orthogonal polynomials: computation and approximation, Ox-
ford University Press, 2004.


 Scritto da in 4 Gennaio 2023  Senza categoria  Commenti disabilitati su Seminario dottorale
Nov 292022
Il calendario delle lezioni è il seguente:

Lunedì 28 novembre dalle 16:00 alle 18:00 Aula B
Martedì 29 novembre dalle 16:00 alle 18:00 Aula A
Mercoledì 30 novembre dalle 16:00 alle 18:00 Aula A
Giovedì 1 dicembre dalle 16:00 alle 18:00 Aula A
Venerdì 2 dicembre dalle 16:00 alle 18:00 Aula A


Many problems in algebra involve the decomposition of certain elements of a ring (or more generally
of a monoid) into a product of certain other elements (hereinafter generically referred to as building
blocks) that are in some sense minimal. The classical theory of factorization investigates factorizations
in which the building blocks are atoms, i.e., non-unit elements of a monoid that are not products of
two non-units. For example, it is well known that every non-zero non-unit of a Dedekind domain (more
generally, of a Noetherian domain) can be written as a finite product of atoms and that in general
such decompositions are not unique. On the other hand, examples of factorizations that lie beyond the
scope of the classical theory include additive decompositions into multiplicative units in rings; cyclic
decompositions of permutations in the symmetric group of degree n; idempotent factorizations of the
“singular elements” of a monoid; and so on.
After an introductory overview of the history and main results in the classical framework, in this
course, we combine the language of monoids and preorders (partial orders that are not necessarily an-
tisymmetric) to make first steps towards the construction of a “unified theory of factorization”. In
particular, we prove an abstract existence theorem that recover, among others, a classical theorem of
Cohn on atomic factorizations in cancellative monoids, a classical result by Anderson and Valdes-Leon
on “irreducible factorizations” in commutative monoids, but also a theorem by Erdos on idempotent fac-
torizations of square singular matrices over fields. We also introduce a notion of “minimal factorization”,
suitable for the new abstract setting, and we qualify and quantify the related non-uniqueness properties
in specific cases but also in some generality. Examples will help to motivate and illustrate the theory.
Prerequisites: Standard knowledge of (basic) algebraic structures and (binary) relations.
Duration of the course: 10 hours.
Exam: Written. Writing of a short essay.
[1] L. Cossu and S. Tringali, Abstract Factorization Theorems with Applications to Idempotent Factor-
izations, e-print (Aug. 2021), arXiv:2108.12379.
[2] L. Cossu and S. Tringali, Factorization under Local Finiteness Conditions, e-print (Aug. 2022),
[3] A. Geroldinger and F. Halter-Koch, Non-Unique Factorizations. Algebraic, Combinatorial and An-
alytic Theory, Pure Appl. Math. 278, Chapman & Hall/CRC, Boca Raton (FL), 2006.
[4] S. Tringali, An Abstract Factorization Theorem and Some Applications, J. Algebra 602 (2022), 352–

 Scritto da in 29 Novembre 2022  Senza categoria  Commenti disabilitati su Seminario dottorale: “Factorizations in monoids and rings”. Laura Cossu – University of Graz
Mar 302021

Seminario di dottorato

Titolo: Introduction to Finite Mixture Models and Latent Class Analysis

Docente: Silvia Columbu, Postdoctoral researcher in Statistics

PhD School of Mathematics and Computer Science, University of Cagliari

Duration: 20 hrs, in the period going from 18th to 26th of February 2021, for a total of 4 CFR


This course is intended as both a theoretical and practical introduction to finite mixtures as a
model based clustering tool. We will introduce the concept of finite mixture of distributions for categorical as
well as continuous variables. We will study the problem of maximum likelihood via expectation-maximization
(EM) algorithms. We will start from simple data structures and then move to the introduction of regressors
and to more complex model structures. We will also explore the problem of model selection and choice of
the number of clusters. We will see practical applications with the aid of devoted packages in the statistical
software R. Students will learn how to implement an analysis and how to read and interpret outputs and
graphical representations of results.


 Scritto da in 30 Marzo 2021  Senza categoria  Commenti disabilitati su Seminario dottorale: Introduction to Finite Mixture Models and Latent Class Analysis, Dott.ssa Silvia Columbu
Nov 162020

Corso di dottorato (20 ore con esame – 4 CFR)

Il dott. Mirko Marras  terrà, a partire dal 9 dicembre 2020, un corso per il dottorato dal titolo “Python for machine Learning Research”.

Le informazioni sono disponibili al seguente  link


Seminario dottorale (20 ore con esame – 4 CFR)


Il prof. Alessandro Buccini terrà, a partire dal 3 giugno 2020, un corso per il dottorato dal titolo “Regularization of ill-posed linear inverse problems”. Le lezioni si terranno online, su una piattaforma che verrà comunicata in seguito, e includeranno alcune sessioni di laboratorio Matlab.
L’abstract del corso è disponibile a questo link.
Ago 042020

L’esame di ammissione per il XXXVI ciclo si svolgerà in modalità telematica per tutti.

Quest’anno è d’obbligo di accludere nella domanda un progetto di ricerca triennale del candidato, la cui discussione sarà la base per la prova orale, svolta in modalità telematica. Per facilitare la stesura del progetto di ricerca, seguono delle linee guida (facoltative) per i curricula di Matematica, e di Informatica e Big Data:

The admission exam for the XXXVI cycle will take place electronically for all candidates.

This year it is compulsory to include in the application a three-year research project of the candidate, whose discussion will be the basis for the oral exam. To facilitate the drafting of the research project, the above links point to (optional) guidelines for the curricula of Mathematics, and of Computer Science and Big Data.

 Scritto da in 4 Agosto 2020  Senza categoria  Commenti disabilitati su Esame di ammissione 2020 – Admission exam 2020
Gen 112020

Il dott. Marco Ortu del DIEE, Università di Cagliari
terrà un corso breve dal titolo:

Leggi di potenza, con applicazioni nell’ingegneria del software

16 Gennaio 2020, ore 9:00 – 14:00 ( ​ Aula C – Dip. di Matematica e Informatica, via Ospedale 72)

Allegata la Locandina

 Scritto da in 11 Gennaio 2020  Senza categoria  Commenti disabilitati su Seminario Dottorale (5 ore con esame – 1 CFU)
Gen 052020

I seminari di Matematica previsti per il mese di Gennaio 2020

sono disponibili in allegato (link)

 Scritto da in 5 Gennaio 2020  Senza categoria  Commenti disabilitati su Seminari Matematica Gennaio 2020
Dic 062019

Seminari matematica

Martedì 10 dicembre ore 16.50 – Aula B

Prof. Andrea Ratto


In questo seminario verranno presentati, con un approccio rivolto a chi non e’  uno specialista del settore, diversi aspetti generali relativi alla teoria delle applicazioni armoniche.

In particolare, si cerchera’ dapprima di dare un’idea dei principali concetti di geometria, topologia e calcolo variazionale che confluiscono nello studio di questi argomenti.

Poi, si passera’ all’illustrazione delle ragioni che rendono significativa questa area di ricerca. Infine, verra’ introdotta la nozione di applicazione poliarmonica e saranno illustrati alcuni problemi e risultati che costituiscono oggetto di ricerche in corso


 Scritto da in 6 Dicembre 2019  Senza categoria  Commenti disabilitati su
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