Corsi 2020/2021


Curriculum in
PhD courses
Title: Partial Differential Equations of Parabolic Type
Lectrurer: Daniele Andreucci
Duration: 24 hours
Period: March-April 2021
Abstract: Initial value and boundary problem for the heat equation and other,
also non-linear, equations of diffusion type.
We'll cover basic existence results, analysis of the asymptotic behavior for
large times, other qualitative properties of the solutions.
Title: Lie algebras, vertex operators, and integer partitions.
Lectrurer: Stefano Capparelli
Duration: 15 hours
Period: Second semester
web page of the course:
Abstract: This is a continuation of the course from last year. This course will be an introduction to the theory of vertex operators and the integer partition theory. The first part of the course will develop integer partition theory and identities of the Rogers-Ramanujan type. The second part will deal with the relatively new concept of vertex operator starting from Lie algebra representations. Finally, we will show the connection between the two theories that at first appear to be very distant. The level of the course will be elementary/introductive, and I will try to keep it essentially self-contained.
Title: Fractional Calculus and Probability
Lectrurer: Mirko D'Ovidio
Duration: 10 hours
Period: February-March
Abstract: We introduce some basic aspects related to fractional calculus and probability. In particular, given a Markov process X and the random time T, we consider the time-changed process X(T) and show that the Cauchy problem for X(T) is written in terms of fractional operators (time and/or space non-local operators). Moreover, we introduce the boundary value problem in the framework of the time changes. That is, we show the connection between multiplicative functionals, semigroups and boundary conditions
monday  february 22   9:00-11:00
monday  march 1        9:00-11:00
monday march 8         9:00-11:00
monday march 15       9:00-11:00
monday march 22       9:00-11:00
link to attend the course:
Title: Introduction to fractals and boundary control problems in irregular domains)
Lectrurers: Anna Chiara Lai, Maria Rosaria Lancia, Raffaela Capitanelli
Duration: 3 CFU+3 CFU+3 CFU
Period: Second semester
First module (Prof. Anna Chiara Lai)
This module presents an introduction to fractals and their mathematical foundations. Motivated by examples and applications, we introduce box counting dimensions, Hausdorff measure and dimension and some methods for their computation. In the second part of the module we focus on particular self-similar fractal structures: we introduce the Iterated Function Systems, we investigate the dimension of the related self-similar sets and we present a dynamical system perspective for this framework. The final part of the module is devoted to the implementation, with Wolfram Mathematica software, of simple visualization and fractal dimension algorithms.
Second module (Maria Rosaria Lancia)
PDES on fractal domains possibly with fractal interfaces.
It is crucial to introduce the trace spaces of Sobolev spaces on fractal sets. ù
We consider boundary value problems with dynamical boundary conditions these are
the most general boundary conditions which include, Dirichlet, Neumann or Robin bcs.
We will look for variational solutions for elliptic problems, regularity properties, asymptotic behaviour, numerical approximation by FEM, parabolic BVPs
Third module (Raffaela Capitanelli)
Nonlinear Analysis on Fractal Structures
This module presents an introduction to some nonlinear problems on fractal structures.
1)  We present existence, uniqueness and approximation results for variational solutions for some quasilinear obstacle problems on domains with a fractal boundary. Our mail tools are suitable extension theorems, sharp quantitative trace results (on polygonal curves) in terms of the increasing numbers of sides and Poincaré type estimates adapted to the geometry.
2)  In order to study mass transport problem on fractal structures, we study the limit of p-Laplace type problems with obstacles as p tends to infinity.
3) Finally, we present some similar asymptotic results on fractal domains like the Sierpinski gasket
Title: Introduction to nonlocal equations
Lectrurer: Maria Medina (Universidad Autonoma de Madrid)
Duration: 10 hours
Period: Room 1B, RM002:  Monday September 13 10:00-12:00 and 15:00-17:00, Tuesday   September 14 10:00-12:00 and 15:00-17:00,  Wednesday September 15 10:00-12:00
Abstract: 1. The fractional Laplacian. - Definitions, probabilistic motivation, limits in s. - Basic properties: maximum principle, example of harmonic function. 2. Fractional Sobolev spaces. - Sobolev inequality, compactness theorem, energy formulation. - Problems in bounded domains. Neumann type boundary conditions. 3. Harmonic extension.
Title: Sobolev Spaces and Applications to Partial Differential Equations
Lectrurer: Anatoli F. Tedeev (South Mathematical Institute of Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia)
Duration: 3CFU
Period: Online: 2021, September 7 (2h), 8 (2h), 10 (4h), 14 (4h), 16 (4h), 17 (2h), 20 (2h), 21 (1h), 22 (1h), 23 (2h), 24 (2h), 27 (2h), 28 (2h), 30 (2h) – please contact Prof. Daniele Andreucci.
Abstract: This course will cover the basic theory of Sobolev Spaces in the Euclidean Space and in Riemannian manifolds. Some more advanced topics will be also introduced, when necessary for the applications, which will refer to problems in unbounded domains of the Euclideanspace orin non-compact Riemannian manifolds.The proposed duration of the course is 2 months, with 16 hours of lectures per month. 1) Sobolev spaces. Basic theory. Approximation by smooth functions. Results of compactness. Embeddings. Poincaré and Hardy inequali-ties. Isoperimetric and Faber-Krahn inequalities. Interplay betweenthe geometry of the manifold and the embedding results. 2) Linear and non-linear diffusion equations; the concept ofsolutionsand the variety of possible behaviors. The energy method. Regulariza-tion and iterative techniques. 3) Asymptotics for large times: classical results in the Euclidean space. The asymptotic profile in linear and nonlinear diffusion. The case of the Neumann problem in subdomains of the Euclidean space. Asymptotic behavior in manifolds.
List of useful courses from the Master degree
Title: Metodi Numerici per l’Ingegneria Biomedica (4 CFU) (Corso di Laurea in Ingegneria Biomedica)
Lectrurer: Francesca Pitolli
Period: November-December 2020

PhD courses
Title:  Analytical Techniques for Wave Phenomena
Lectrurer: Paolo Burghignoli
Duration: 6 CFU
Period: from 28 September to 28 October 2021, online,
Abstract: The course aims at providing Ph.D. students with analytical tools useful in applied research on general wave phenomena. The unifying theme is that of complex analysis, of which a compact, self‐contained introduction is presented. Fundamental techniques asymptotic techniques are then illustrated, including ray optics and the Laplace and saddle‐point methods for the asymptotic evaluation of integrals. Applications are focused on the analysis of both time‐harmonic and transient waves excited in planar layered structures by canonical sources. As concerns the former, different wave species will be defined and physically discussed (space, surface, leaky, lateral waves). As concerns the latter, the Cagniard‐de Hoop method will be introduced.
Title:  Corso di scrittura tecnico-scientifica
Lectrurer: Emilio Matricciani (Politecnico di Milano)
Duration: 3 CFU
Period: January-February 2021
1) Il canale di comunicazione. Canali virtuali e canali trasparenti. La comunicazione scritta: linguaggio analogico e digitale, testo e figure, principi generali dell’elaborazione visiva e testuale. Il canale di comunicazione e i disturbi. La qualità del manoscritto tecnico-scientifico.
2) L'eredità dei giganti: l'articolo e le riviste scientifiche. Nascita e sviluppo della scrittura tecnico-scientifica. Evoluzione della struttura canonica. Risultati da vedere: tabelle e figure. Scrittura e creatività. Esempi storici.
3) La pianificazione strategica del manoscritto scientifico. Le tre funzioni del manoscritto. Struttura fondamentale del manoscritto (informativo, persuasivo, motivazionale). Organizzazione e indice del manoscritto. La struttura canonica.
4) Dalla prima versione alla versione definitiva. Revisione del contenuto, dei paragrafi, delle frasi, delle parole. Formule di leggibilità.
5) Scrivere e pubblicare. Scientometria e indici bibliometrici. Riviste scientifiche e revisione di un articolo. Etica e frodi scientifiche.
Title: Nanophotonics and Plasmonics 
Lectrurer: Concita Sibilia
Duration: 2 CFU
Period: Second semester
The part of seminars related to Nanophotonics aims to introduce to students some exciting concepts that differ from conventional wave optics, with particular emphasis to the role of the evanescent fields in many practical applications, such as near field optical microscopy. The field of plasmonics (interaction of light with electrons in metals) has attracted a great deal of interest over the past two decades, but despite the many fundamental breakthroughs and exciting science it has produced, it is yet to deliver on the applications that were initially targeted as most promising. The seminars proposed examine the primary fundamental hurdles in the physics of plasmons that have been hampering practical applications and highlights some of the promising areas in which the field of plasmonics can realistically deliver.
Title:  Basics of Nonlinear Optics
Lectrurer: Concita Sibilia
Duration: 2 CFU
Period: Second semester
Abstract: Nonlinear Optics (NLO) is the study of phenomena that occur as a consequence of the modification of the optical properties of a material system by the presence of light. Basics and more recent applications of NLO to new light sources and devices will be presented in a series of seminars.
List of useful courses from the Master degree
Title: Microwaves
Lectrurers:Marta Cavagnaro, Fabrizio Frezza, Alessandro Galli
Duration: 9 CFU
Period: First semester
Title:  Artificial materials, metamaterials and plasmonics for electromagnetic applications
Lectrurers: Fabrizio Frezza
Duration: 6 CFU
Period: First semester
Title:    Molecular dynamics and atomistic simulations
Lectrurers: Giuseppe Zollo
Duration: 6 CFU
Period: First semester
Title:    Advanced Electromagnetics and Scattering
Lectrurers: Fabrizio Frezza
Duration: 6 CFU
Period: Second semester
Title:    Laser Fundamentals
Lectrurers: Concita Sibilia
Duration: 6 CFU
Period: Second semester
Title:    Quantum Information, I e II
Lectrurer: Fabio Bovino (Leonardo SpA)
Duration: 5+5 CFU
Period: Second semester
Title:    Lavorare in team, project management,
Lectrurer: Giancarlo Mammetti
Curriculum in
PhD courses
Title: Radiation-Matter Interaction, Photoemission and Photoabsorption Spectroscopy
Lectrurers: Carlo Mariani, Settimio Mobilio, Francesco Offi, Alessandro Ruocco
Duration: 32 hours
Period: February-May 2021
Abstract: Introduction to the photoelectron spectroscopy: theoretical background, the three-step model, atoms and molecules, low-dimensional solid systems, experiments with angular resolution, time-resolved experiments. Instrumentation: charged particles, Auger electron spectroscopy and resonant photoemission. Theoretical background of absorption. Multiple scattering theory: a method for the observation of the electronic states and spectroscopy
measurements. Surfaces and low-dimensional systems, electronic properties. Core-level photoemission and surface core-level shifts. Angular resolved photoemission, electronic band structure. Band structure of exemplary 1D and 2D systems. Electromagnetic radiation sources, synchrotron radiation. Introduction to the free-electron laser: a coherent source of radiation from UV to X rays. X ray absorption spectroscopy, EXAFS and XANES: fundamentals and applications. X ray elastic and anelastic scattering.
List of useful courses from the Master degrees
Title: Surface Physics and Nanostructures (6 CFU) (Corso di Laurea in Fisica)
Lectrurer: Maria Grazia Betti
Planned period: October-December 2020
Title: Chimica Fisica dello Stato Solido e dei Materiali Nanostrutturati (6 CFU) (Corso di Laurea in Chimica Industriale) 
Lectrurer:  Danilo Dini
Planned period: October-December 2020
Title: Sistemi di produzione ed accumulo dell'energia (9 CFU) (Corso di Laurea in Chimica Industriale) 
Lectrurer:  Maria Assunta Navarra
Planned period: October-December 2020
Title: Fabbricazione e caratterizzazione di nanostrutture (6 CFU) (Corso di Laurea in Ingegneria delle Nanotecnologie) 
Lectrurer:  Carlo Mariani
Planned period: March-June 2021
Title: Laboratorio Macromolecole (9 CFU) (Corso di Laurea in Chimica Industriale) 
Lectrurer:  Andrea Martinelli
Planned period: March-June 2021
Title: Microscopie e tecniche di nanocaratterizzazione (9 CFU) (Corso di Laurea in Ingegneria delle Nanotecnologie) 
Lectrurer:  Marco Rossi
Planned period: March-June 2021
Title: Chimica dei materiali polimerici (6 CFU) (Corso di Laurea in Chimica Analitica) 
Lectrurer:  Ilaria Fratoddi
Planned period: March-June 2021
Title: Electron Microscopy and Related Techniques (9 CFU) (Corso di Laurea in Nanotechnology Engineering) 
Lectrurer:  Daniele Passeri
Planned period: March-June 2021

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