COURSES 2021/2022
Curriculum in
MATEMATICA PER L'INGEGNERIA /MATHEMATICS FOR ENGINEERING
PhD courses
Title: Representations and Number Theory
Lecturers: Stefano Capparelli, Pietro Mercuri
Duration: 24 hours
Period: Room 1E, RM004, 15:30-18:00, 2022 March 08 and 15, April 5, 12 and 26, May 3, 10, 19, 26, June 7 and 21
Abstract: In this course we will examine recent litarature that links representation theory of Lie algebras and Number Theory. In particular we shall examine:
- Nandi,D: Partition identities arising from Standard A_{2}^{(2)}-modules of level 4, Rutgers PhD Thesis 2014
- Konan, I.: Identités de type Rogers-Ramanujan: preuves bijectives et approche à la théorie de Lie, PhD Thesis, Université de Paris, 2020.
- Capparelli, Meurman, Primc,Primc: New partition identities from C_{l}^{(1)}-modules, arXiv:2106.06262
Title: Variational problems for nonlinear Schrodinger equations on metric graphs
Lecturer: Simone Dovetta
Duration: 15 hours
Period: Online, May 9 15:00-17:00, May 10 15:00-17:00, May 12 15:00-17:00 May 24 15:00-17:00, May 30 15:00-17:00, May 31 15:00-17:00, June 1 15:00-18:00
Abstract: Since their first appearance in physical chemistry in 1953, networks (or metric graphs) have been proposed to model almost one-dimensional ramified structures. Despite being more than sixty years old, it is within the last two decades that the theory of evolution on networks became popular, mainly driven by the ubiquity of networks in applications, from quantum mechanics to fluid dynamics, from nonlinear optics to traffic regulation. The aim of this course is to give an introductory overview of recent results for nonlinear Schrödinger equations on metric graphs. In particular, we will consider variational problems for the energy functional under the mass constraint on a given graph. The focus will be set on the minimization problem: does the above energy admit global minimizers? What is the role of We will see that the answers to these questions are strongly sensitive to the specific properties of the graphs.
Title: Fractional Calculus and Probability, I
Lecturer: Mirko D'Ovidio, Raffaela Capitanelli
Duration: 15+5 hours
Period: Part 1: January 2022, Part 2: February 2022
Abstract: In Part 1, we introduce some basic aspects related to fractional calculus and probability. In particular, we consider time-changed Markov processes driven by Cauchy problems written in terms of non-local (time and/or space) operators. Moreover, we consider the boundary value problem in the framework of the time changes and in general, we show some connection between multiplicative functionals, semigroups and boundary value problems for PDEs and non-local PDEs. We introduce some basic notions about limit theorems, stochastic processes, PDEs connections, non-local operators with special attention for the case of fractional (Caputo) derivative and fractional Laplacian, additive and multiplicative functionals associated with boundary conditions, time changes associated with boundary conditions. We focus on Dirichlet, Neumann, Robin and Wentzell boundary conditions together with the probabilistic reading of killed, reflected, elastic and sticky processes. We also discuss some applications concerned with regular and irregular domains in the macroscopic analysis introduced by fractional equations. In Part 2, we discuss provide approximation results for space-time non-local equations with general non-local (and fractional) operators in space and time. We consider a general Markov process time changed with general subordinators or inverses to general subordinators. Our analysis is based on Bernstein symbols and Dirichlet forms, where the symbols characterize the time changes, and the Dirichlet forms characterize the Markov processes.
Title: Fractional Calculus and Probability, II
Lecturers: Maria Rosaria Lancia, Anna Chiara Lai .
Duration: 4+4 hours
Period: March-May 2022
Abstract: We introduce the regional fractional Laplacian in extension domains, possibly with an irregular boundary. A fractional Green formula will be proved. We discuss some evolution BVPs with either Dirichlet, or Neumann or Robin type boundary conditions, possibly non local. Existence, uniqueness of the weak solution will be discussed as well as regularity properties of the associated semigroup. A comparison with the different definitions of fractional Laplacian will also be addressed. We also present some results in the framework of fractional compartmental epidemic models, with particular attention to Caputo-type fractional SIS models. We begin with a brief introduction to some compartmental epidemic models and with the derivation of the SIS model in the ordinary case. We then focus on the fractional SIS models based on the fractional Caputo derivative. Assuming the conservation of the total population, we discuss the equilibria of the system and we prove the existence and uniqueness of the solution. We finally present a local series representation for the solution.
Title: Introduction to hyperbolic conservation laws and applications
Lecturer: Elisa Iacomini (Aachen University)
Duration: 10 hours
Period: 7, 8, 11, 14, and 16 February, 2022, 10:00-12:00, Room 1B, RM002
Abstract: This course offers an overview of the theory of hyperbolic conservation laws and the related numerical methods. Conservation laws are essential for understanding the physical world around us, indeed they describe the conservation in time of a quantity in an isolated system. Starting from the linear case, we generalize the theory of characteristics analyzing the Riemann problem in details. Due to the nonlinearity of the problem, we will deal with the study of weak solutions, face the problem of non uniqueness of solutions and end up with the concept of entropy solution.
Then, we will focus on the numerical counterpart, in particular we will consider the so-called shock-capturing methods. We will investigate their main properties as consistency, stability and convergence.
As modelling example, we will focus mainly on vehicular traffic flow models.
Title: Spectral geometry of the Laplace operator
Lecturers: Luigi Provenzano, Alessandro Savo
Duration: 12 hours
Period: Second Semester
Abstract: In the first part of the course, we will provide a brief introduction to the spectrum of the Laplacian with various boundary conditions, and to the spectrum of the Dirichlet-to-Neumann map. This includes a discussion of the functional setting of these problems, and a few basic examples. Then, we will focus on some classical problems in spectral geometry, such as eigenvalue bounds and isoperimetric inequalities for the eigenvalues. In particular, we will present a set of techniques for their study. In the final part, if time allows, we will consider the same kind of problems for the Laplacian with a magnetic field, and we will discuss some recent developments on this topic.
Title: Inverse problems and time-fractional partial differential equations
Lecturer: Masahiro Yamamoto (Tokyo University)
Duration: 16 hours
Period: 2022, Aula 1B1, 14, 20, 22, 27, 28 September (10:00-12:00) and 4, 5, 7 October (10:00-12:00) Abstract: We consider an initial boundary value problem for time-fractional diffusion-wave equation:
The idea of fractional derivatives dates back to Leibnizand there have been many works including by Abel, Riemann, Liouville. Now the system (*) is widely recognized as more feasible model for various phenomena such as anomalous diffusion in heterogeneous media, where the anomaly cannot be well interpreted by the classical advection. diffusion equation and the conventional models often provide wrong simulation results. Thus we have to exploit more relevant models because the issues are serious, for example, for the protection of the environments , and the mathematical researches should support such practical applications.
For researches on inverse problems, we need also mathematical analyses for (*). Usually in practice, we are not a priori given coefficients and other quantities in (*). The inverse problems are concerned with parameter identification, and are essential for more accurate prediction or simulations of anomalous diffusion. Therefore mathematical researches should be done for both foundations of direct problems and applications to inverse problems for (*).
List of useful courses from undergraduate programmes
Title: Metodi Numerici per l’Ingegneria Biomedica (4 CFU) (Corso di Laurea in Ingegneria Biomedica)
Lecturer: Francesca Pitolli
Planned period: November-December 2020
Curriculum in
ELETTROMAGNETISMO/ELECTROMAGNETISM
PhD courses
Title: Analytical Techniques for Wave Phenomena
Lecturer: Paolo Burghignoli
Duration: 6 CFU
Period: from 28 September to 28 October 2021, online, https://www.youtube.com/playlist?list=PLKM6nRpY51X1fq6KltiOuNZnp7xIRbGAO
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 for the asymptotic evaluation of integrals are then illustrated, including the Laplace and saddle‐point methods. Applications are focused on the analysis of time‐harmonic waves excited in planar layered structures by canonical sources and on scattering of plane waves from half planes. As concerns the former, different wave species will be defined and physically discussed (space waves, surface waves, leaky waves, lateral waves). As concerns the latter, the Wiener‐Hopf method will be introduced.
Title: Corso di scrittura tecnico-scientifica
Lecturer: Emilio Matricciani (Politecnico di Milano)
Duration: 3 CFU
Period: 8-9 e 15-16 febbraio 2022, Facoltà di Ingegneria, Edificio di San Pietro in Vincoli
Abstract:
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
Lecturer: 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
Lecturer: 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
Lecturers: Marta Cavagnaro, Fabrizio Frezza, Alessandro Galli
Duration: 9 CFU
Period: First semester
Title: Artificial materials, metamaterials and plasmonics for electromagnetic applications
Lecturers: Fabrizio Frezza
Duration: 6 CFU
Period: First semester
Title: Molecular dynamics and atomistic simulations
Lecturers: Giuseppe Zollo
Duration: 6 CFU
Period: First semester
Title: Advanced Electromagnetics and Scattering
Lecturers: Fabrizio Frezza
Duration: 6 CFU
Period: Second semester
Title: Laser Fundamentals
Lecturers: Concita Sibilia
Duration: 6 CFU
Period: Second semester
Title: Quantum Information, I e II
Lecturer: Fabio Bovino (Leonardo SpA)
Duration: 5+5 CFU
Period: Second semester
Curriculum in
SCIENZA DEI MATERIALI / MATERIALS SCIENCE
PhD courses
Titolo Radiation-Matter Interaction, Photoemission and Photoabsorption Spectroscopy
Lecturers: Carlo Mariani, Settimio Mobilio, Francesco Offi, Alessandro Ruocco
Duration: 32 hours
Period: February-May 2022
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)
Lecturer: Carlo Mariani
Planned period: October-December 2021
Title: Chimica Fisica dello Stato Solido e dei Materiali Nanostrutturati (6 CFU) (Corso di Laurea in Chimica Industriale)
Lecturer: Danilo Dini
Planned period: October-December 2021
Title: Sistemi di produzione ed accumulo dell'energia (9 CFU) (Corso di Laurea in Chimica Industriale)
Lecturer: Maria Assunta Navarra
Planned period: October-December 2021
Title: Fabbricazione e caratterizzazione di nanostrutture (6 CFU) (Corso di Laurea in Ingegneria delle Nanotecnologie)
Lecturer: Carlo Mariani - Ernesto Placidi
Planned period: March-June 2022
Title: Laboratorio Macromolecole (9 CFU) (Corso di Laurea in Chimica Industriale)
Lecturer: Andrea Martinelli
Planned period: March-June 2022
Title: Physics Laboratory II (9 CFU) (Corso di Laurea in Fisica)
Lecturer: Carlo Mariani
Planned period: March-June 2022
Title: Microscopie e tecniche di nanocaratterizzazione (9 CFU) (Corso di Laurea in Ingegneria delle Nanotecnologie)
Lecturer: Marco Rossi
Planned period: March-June 2022
Title: Chimica dei materiali polimerici (6 CFU) (Corso di Laurea in Chimica Analitica)
Lecturer: Ilaria Fratoddi
Planned period: March-June 2022
Title: Scanning Probe Microscopy (3 CFU) (Corso di Laurea in Nanotechnology Engineering)
Lecturer: Daniele Passeri
Planned period: March-June 2022