Dottorato in MODELLI MATEMATICI PER L'INGEGNERIA, ELETTROMAGNETISMO E
NANOSCIENZE

Ph.D. COURSES

 

Neural Networks & Machine Learning
- Schedule: 04-06/2026, TBD
- Hours: 30
- Lecturer: Adriano BARRA (Sapienza)
- Abstract: he course follows a historical perspective and analyzes explicit mathematical models and methods related to information processing spontaneously achieved by networks of neurons (biological or artificial). After a brief reviewing of key concepts stemming in statistical mechanics, stochastic processes and statistical inference, we start from the first models for the emission of an electrical signal from a single neuron, to move toward the study of their interactions in simple neural architectures, analyzing the statistical learning capabilities that these networks enjoy. In particular, due to the Nobel Prize in Physics awarded in 2024 to John Hopfield and Geoffrey Hinton for their pioneering studies on neural networks, particular emphasis will be placed on their contributions and on the close connections that exist between them. The methodological leitmotif will be the statistical mechanics of complex systems (i.e. Parisi's theory, Nobel Prize in Physics in 2021) with its associated package of observables and typical tools (replicas, overlaps, cavity fields, etc.).
- Verification: Oral
- Notes: Intereseted students are invited to contact the Lecturer (adriano.barra@uniroma1.it).

MINICOURSES AND SEMINAR SERIES

 

USEFUL COURSES FROM OTHER PROGRAMMES

See the list of PhD Courses related to Mathematics in the Rome area.
 

Metodi Numerici per l'Ingegneria Biomedica (Laurea Magistrale in Ingegneria Biomedica)
- Schedule: first semester 
- Hours 30+30
- Lecturer: Francesca PITOLLI (Sapienza)
- Abstract: Prima parte: Metodi numerici per la soluzione di problemi differenziali, metodi di Runge-Kutta, metodi alle differenze finite (30 ore). Seconda parte: Approssimazione ai minimi quadrati per l'identificazione di un modello e la stima dei parametri. Soluzione di sistemi lineari sovradeterminati. Decomposizione ai valori singolari e sue applicazioni. Problemi inversi mal posti e tecniche di regolarizzazione. Soluzione di sistemi lineari sottodeterminati. Analisi delle componenti principali e sue applicazioni (30 ore). Per ogni argomento verranno svolte delle esercitazioni in cui si utilizzeranno i metodi numerici illustrati a lezione per risolvere alcuni problemi applicativi.
 

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CURRICULUM: MATERIALS SCIENCE
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Ph.D. COURSES
 

Radiation-Matter Interaction, Photoemission and Photoabsorption Spectroscopy, I

- Schedule: 02-03/2025, U. Roma 3, TBD
- Hours: 12
- Lecturers: Carlo MARIANI (Sapienza), Settimio MOBILIO (Roma Tre), Francesco OFFI (Roma Tre), Alessandro RUOCCO (Roma Tre)
- 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. 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.
- Verification: oral presentation of a current research topic which uses the methods presented in the course.
- Notes: 

Radiation-Matter Interaction, Photoemission and Photoabsorption Spectroscopy, II
- Schedule: 03-04/2025, Sapienza, TBD
- Hours: 20
- Lecturer: Carlo MARIANI (Sapienza), Settimio MOBILIO (Roma Tre), Francesco Offi (Roma Tre), Alessandro Ruocco (Roma Tre)
- Abstract: Electromagnetic radiation sources, synchrotron radiation, theoretical background, storage rings, beamlines, photoemission. Introduction to the free-electron laser: a coherent source of radiation from UV to X rays. X ray absorption spectroscopy, theoretical background of absorption. Multiple scattering theory: a method for the observation of the electronic states and spectroscopy measurements. EXAFS and XANES/NEXAFS: fundamentals and applications. X ray elastic and anelastic scattering. High energy photoemission, application to buried interfaces/materials.
- Verification: oral presentation of a current research topic which uses the methods presented in the course.

Advances in Raman spectroscopy: from traditional vibrational spectroscopy to surface enhanced approaches
- Schedule: 04-05/2026, TBD
- Hours: 10
- Lecturer: Angela CAPOCEFALO (U. L'Aquila)
- Abstract: The aim of the course is to provide doctoral students with a thorough understanding of Raman spectroscopy, covering both the traditional technique and the more advanced surface enhanced Raman spectroscopy. After introducing the fundamentals of the Raman scattering, the experimental aspects of the technique will be examined, including the description of the measurement apparatus and the analysis and interpretation of data. Surface enhanced Raman spectroscopy will be then introduced, discussing the different mechanisms underlying signal amplification. The plasmonic properties of commonly used nanostructured metal substrates and the recent advances in the technique, such as tip-enhanced Raman spectroscopy will be presented. Finally, innovative applications of the technique in various research fields such as sensing, nanomedicine, materials science, and cultural heritage will be discussed.
- Verification: oral presentation of a current research topic which uses the methods presented in the course.

- Introduction to Optical Spectroscopic Techniques and Applications to Low Dimensional Semiconductors
- Schedule: 02-05/2026, TBD
- Hours: 30
- Lecturer: Elena STELLINO (Sapienza)
- Abstract: The course aims to introduce three of the most common techniques in optical spectroscopy (Infrared, Raman, and photoluminescence) by providing a comprehensive approach that begins with theoretical foundations and then leads the students to handle real experimental cases. The key objectives of the course include:
• gain familiarity with the theoretical framework underpinning the presented spectroscopic techniques, covering phenomenology, classical models, and some aspects of the quantum approach;
• identify what kind of physical information can be extracted from the theoretical models;
• understand the working principles governing the setups used in experiments;
• engage in actual experimental work within research laboratories specialized in optical spectroscopies. This involves sample preparation, data acquisition, and the use of softwares for the data analysis.
The course comprises frontal lessons (50%) and supervised laboratory experiences with data analysis activities (50%). The laboratory sessions will focus on samples belonging to the class of 2D semiconductors, exposing students to one of the most studied research topics in the field of material science.
- Verification: Students, organized into groups, will prepare written reports for each module detailing the laboratory experience, scientific case, experimental setup, data analysis, and result interpretation. Finally, e ach student will present and discuss a scientific article from the literature that utilizes one of the discussed techniques.

USEFUL COURSES FROM OTHER PROGRAMMES
 

Surface Physics and Nanostructures (Corso di Laurea in Fisica)
- Lecturer: Carlo Mariani (Sapienza)
- Duration: 6 CFU
- Period: first semester
- Abstract: From surfaces to new atomic and molecular architectures - 1D and 2D systems - Low-dimensional crystalline structures – Symmetries – Surface thermodynamics - Relaxation and reconstruction processes - Structural properties and techniques (AFM, STM, LEED, GIXD) - Electronic properties (electron gas, band structure) of nanostructures- Giant magnetoresistance - Electron spectroscopic techniques (angular-resolved photoelectron spectroscopy, ...) - Electronic properties and structure of nanostructures: etherostructures, nano-wires, self-assembled monolayers) – Graphene: electronic states, structure, supported graphene, growth, characterization, doping, ...).

Chimica Fisica dello Stato Solido e dei Materiali Nanostrutturati (Corso di Laurea in Chimica Industriale)
- Lecturer: Danilo Dini (Sapienza)
- Duration: 6 CFU
- Schedule: first semester
- Abstract: I contenuti del corso includono la descrizione della materia allo stato solido e l'analisi delle strutture cristalline di sistemi prototipici sulla base di considerazioni di tipo energetico tenendo conto dei legami caratteristici che tengono insieme i materiali allo stato solido. Viene inoltre offerta una analisi delle proprietà vibrazionali dei solidi e come queste controllano le propreta' termodinamiche dei sistemi solidi. Il corso comprende anche l'analisi dei fattori alla base dei fenomeni di conducibilità elettrica nei solidi e delle proprietà elettrochimiche di stato solido. Analisi delle proprietà dei sistemi nanostrutturati con particolare riferimento ai nanotubi di carbonio. 

Sistemi di produzione ed accumulo dell'energia (Corso di Laurea in Chimica Industriale, in Italian)
- Lecturer: Maria Assunta Navarra (Sapienza)
- Duration: 9 CFU
- Period: first semester
- Abstract: Il corso si inquadra nei processi formativi in ambito industriale e applicativo specifici del Corso di Laurea. Il corso intende ampliare le conoscenze proprie della Chimica Fisica e dell’Elettrochimica, con particolare riguardo alle problematiche energetiche e agli aspetti di gestione delle risorse. I contenuti concettuali e metodologici sono spesso affiancati da riferimenti agli aspetti economici e applicativi. Particolare enfasi è data alle metodologie più moderne per lo studio di sistemi avanzati di accumulo e conversione dell’energia per via elettrochimica. Viene introdotto il concetto di smart grid e della produzione di energia da fonti rinnovabili sostenuta da opportuni sistemi di accumulo.
- link: https://elearning.uniroma1.it/course/view.php?id=11703

Laboratorio Macromolecole (Corso di Laurea in Chimica Industriale)
- Lecturer: Andrea Martinelli (Sapienza)
- Duration: 9 CFU
- Period: second semester
- Abstract: Il corso è strutturato in modo da fornire informazioni su alcune tecniche sperimentali impiegate per la caratterizzazione dei materiali polimerici. Ogni argomento trattato si sviluppa in tre fasi: (1) esame delle grandezze che si misurano con la tecnica strumentale in oggetto e le teorie che descrivono i fenomeni analizzati; (2) descrizione della strumentazione impiegata e le modalità sperimentali da utilizzare in relazione alle informazioni che si vogliono acquisire; (3) prove sperimentali e acquisizione dei dati per la successiva elaborazione. I risultati ottenuti verranno analizzati in base alle teorie descritte nella prima fase.

Microscopies and nanocharacterization techniques
- Lecturer: Marco Rossi (Sapienza)
- Duration: 9 CFU
- Period: second semester
- Abstract: The course provides students with essential skills in various microscopy techniques that are essential for R&D and industrial processes using nanotechnologies. It covers electron and scanning probe microscopy, spectroscopy and atomic scale materials characterisation. The course aims to enable the participants to select the best techniques for nano-characterisation. It includes training in electron optics, interpretation of results, and various microscopy (and also spectroscopical) methods for analysing chemical, structural and physical properties. The course also emphasises critical skills, communication, ethical judgement and continuous learning, preparing students for professional challenges in nanotechnology and related fields.

Chimica e caratterizzazione dei materiali polimerici (Corso di Laurea in Chimica Analitica)
- Lecturer: Ilaria Fratoddi (Sapienza)
- Duration: 6 CFU
- Period: second semester
- Abstract: Chimica dei polimeri, metodiche di caratterizzazione, materiali nanostrutturati (principalmente polimeri, ma anche qualche altro outsider).

- Title: Scanning Probe Microscopy (Corso di Laurea in Nanotechnology Engineering)
- Lecturer: Daniele Passeri (Sapienza)
- Duration: 3 CFU
- Period: second semester
-Abstract: Fondamenti di AFM e SPM. Tecniche avanzate basate su AFM. Microscopia ad effetto tunnel. Scanning near-field optical microscopy (SNOM). Tip-enhanced Raman spectroscopy (TERS). Litografia mediante AFM.

 

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CURRICULUM: ELECTROMAGNETISM
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Ph.D. COURSES
 

Nanophotonics and Plasmonics
- Schedule: 03-04/2026 - the schedule will be agreed with interested students, please contact concita.sibilia@uniroma1.it
- Hours: 20
- Lecturer: Concita SIBILIA
- Abstract: 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.
- Verification: Oral discussion of course's topics.

Basics of Nonlinear Optics
- Schedule: 04-05/2026 - the schedule will be agreed with interested students, please contact concita.sibilia@uniroma1.it
- Hours: 20
- Lecturer: Concita SIBILIA
- 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.
- Verification: Oral discussion of course's topics.

Experiences in Optics
- Schedule: 12/2025-02/2026, TBD - the schedule will be agreed with interested students, please contact alessandro.belardini@uniroma1.it
- Hours: 20
- Lecturer: Alessandro BELARDINI (Sapienza)
- Abstract: The course gives the theoretical basis of optics, geometrical optics and physical optics, polarisation, diffraction, interference, use of simple optical elements such as lenses, prisms, polarisers, waveplate. After the theoretical introduction, the course provides a series of optics laboratory experiences were the students can experimentally verify the laws of optics that they have studied. The experiences are divided into three groups. The first concerns geometric optics, in particular Snell's law. The second and third groups concern physical optics, in particular polarization, interference and diffraction.
- Verification: Oral discussion of course's topics.

Numerical methods for simulations of electromagnetic wave – matter interactions
- Schedule: 12/2025-02/2026, TBD - the schedule will be agreed with interested students, please contact emilija.petronijevic@uniroma1.it
- Hours: 20
- Lecturer: Emilija PETRONIJEVIC (Sapienza)
- Abstract: The course gives practical basis for the numerical investigation of interaction between matter and electromagnetic waves in different spectral ranges. After the theoretical introduction focusing on finite difference time domain, the course makes use of a commercial solver to show how different materials, in micro-and nanoscaled geometries, tailor electromagnetic wave distribution. The course then provides two simulation experiences: the first treats a single nanostructure, and the second periodically organized nanostructures. Both experiences treat transmission and absorption of the waves, near- and far-field spatial and spectral properties, electromagnetic behavior at resonances, and the influence of the excitation wave polarization.
- Verification: discussion of a course topic
 

USEFUL COURSES FROM OTHER PROGRAMMES
 

Analytical Techniques for Wave Phenomena (PhD Program in Information and Communication Technology)
- Period: 09-10/2026, TBD
- Hours: 36
- Lecturer: Paolo Burghignoli
- 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 from half planes and spheres. 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 and the Watson transformation will be introduced.
- Verification: Oral discussion of course's topics.

Thermal Radiation and Infrared Signature (Master in Optics and Quantum Information)
- Period: January-March 2025, see the Master web page.
- Hours: 30
- Lecturer: Roberto Li Voti (Sapienza)
- Abstract: The course will cover the following topics: spontaneous emission, thermal radiation, Planck's law, Stephan-Bolzmann law. Emissivity, black body theory and selective radiators. Electromagnetic spectrum, light radiation, infrared radiation. Characteristic parameters of a radiant element: radiance, spectral radiance, power, spectral power. Propagation of the light signal in air, atmospheric absorption bands. Atmospheric effects: absorption, self-emission, diffusion, deflection, turbulence. Numerical techniques for the evaluation of the variable emissivity of materials; and nondestructive photoacoustic and photothermal techniques for the characterization of materials.

Laboratory for Industrial Applications of Photothermal and Photoacoustic Optical Technologies (Master in Optics and Quantum Information)
- Lecturer: Roberto Li Voti (Sapienza)
- Hours: 30
- Period: March-May 2025,  see the Master web page.
- Abstract: The course will provide the theoretical bases of the photothermal, photoacoustic, radiometric, and infrared techniques for nondestructive evaluation and testing of materials (nanomaterials and metamaterials). Many applications will be introduced in different fields: industry, environment, energy, but also biology, medicine, agrifood. Final comparisons will be introduced among the diagnostic techniques. The course also contains some experimental activities in the laboratory and the relative data analysis and data processing.

Optics (LM Nanotechnology)
- Lecturer: Eugenio Fazio
- Duration: 6 CFU
- Period: second semester
- Abstract: see the course web page

Molecular dynamics and atomistic simulations (LM Nanotechnology)
- Lecturer: Giuseppe Zollo
- Duration: 3+3 CFU: Statistical physics and Monte Carlo Techniques (3 cfu), Molecular Dynamics (3 cfu)
- Period: first semester
- Abstract: The main purpose of the course is to transfer to the students the basic knowledge concerning the multidisciplinary topics that are the basis of the atomistic simulations techniques and methods. The course is focused on the main aspects of the classical models with a brief mention to the quantum mechanical approaches.

Laser Fundamentals (LM Electronic Engineering)
- Lecturer: Concita Sibilia
- Duration: 6 CFU
- Period: Second semester
- Abstract: The purpose of the course is to provide the student with an understanding of the working principles of active optical devices based on the interaction of light with nanoscale systems; It also wants to provide a knowledge of the most current techniques of design and realization of pulsed lasers, including miniaturized lasers (q-dots, photonic crystal lasers) and their uses in the field of Optoelectronics, quantum information and also in diagnostics employing the miniaturized Optical sources.

Quantum Information, I (Master in Optics and Quantum Information)
- Lecturer: Fabio Bovino
- Duration: 5 CFU
- Period: first semester,  see the Master web page
- Abstract: Classical Electrodynamics: fundamental equations and dynamical variables. Quantum Electrodynamics in the Coulomb Gauge: general framework, time evolution, observables and states of the quantized free field, the Hamiltonian for the Interaction between particles and field. Coherent interaction: two state dynamics, Jaynes-Cummings model. Quantum Statistics of the field. Dissipative processes. Dressed states.

Quantum Information, II (Master in Optics and Quantum Information)
- Lecturer: Fabio Bovino
- Duration: 5 CFU
- Period: second semester,  see the Master web page.
- Abstract: Finite-Dimensional Hilbert Spaces: Quantum bits, Multiple qubits, Quantum Tomography, Entanglement, Bell Inequality, Teleportation, Nocloning. Quantum Information - Theory: Entropy and Information, the Holevo Bound, Communication over noise quantum channels, entanglement as physical resource. Quantum dense coding and quantum cryptography. Infinite-Dimensional Hilbert Spaces.

Advanced Electromagnetics and Scattering (LM Electronic Engineering)
- Lecturer: Fabrizio Frezza
- Duration: 6 CFU
- Period: second semester
- Abstract: The course is aimed to present an overview of some advanced topics in Electromagnetics, of considerable importance for the applications, and an introduction to electromagnetic scattering. Key instruments extensively used for their physical intuition and representative power are the modal expansion with the relevant equivalent distributed circuits, and the plane‐wave spectra. The concepts of Green’s function and integral representation are also studied in depth.

Microwaves (LM Electronic Engineering)
- Lecturers: Marta Cavagnaro (Sapienza), Fabrizio Frezza (Sapienza)
- Duration: 9 CFU
- Period: first semester
- Abstract: Scope of the Course is to provide the student with both the basic knowledge concerning guided propagation of electromagnetic fields, and the most important microwave structures and circuits. In particular, the teaching will deal with distributed-constant analysis, typical of microwave circuits; an overview of the principal microwave guiding structures and circuit elements, and the methodologies to analyze them.

Artificial materials, metamaterials and plasmonics for electromagnetic applications (LM Electronic Engineering)
- Lecturer: Fabrizio Frezza (Sapienza)
- Duration: 6 CFU
- Abstract: The Course is aimed to provide the general electromagnetic theory of artificial materials, metamaterials and plasmonic structures, of considerable importance in many recent applications.