In considerazione dell’impegno richiesto allo studente, i corsi di dottorato sono valutati, in termini di rapporto tra CFU e ore di didattica frontale, circa il 50% in più rispetto ai corsi di laurea magistrale.
Per organizzazione e regole didattiche, si veda "Offerta formativa programmata a.a. 2023/24".
Le seguenti informazioni sono fornite nella lingua corrispondente a quella in cui i corsi sono tenuti.
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CURRICULUM: MATHEMATICS FOR ENGINEERING
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* Ph.D. courses
Title: Quiver representations
Lecturer: Ralf Schiffler (University of Connecticut)
Duration: 20 hrs, 3 CFU
Place: Aula 1B/1, pal. RM002 (via Scarpa 16)
Day and time of the lectures:
First lecture: Monday May 6th
Every Monday from 2:30pm to 4:30pm
Every Wednesday from 10am to 12 am
Last lecture: Wednesday June 5th
Abstract: This course is an introduction to quivers and their representations, with a focus on applications to the representation theory of finite dimensional algebras. Topics covered in the course include: representations of quivers, direct sums, morphisms, kernels, exact sequences, projective and injective representations, Auslander-Reiten quiver, algebras, modules, idempotents, path algebras, Auslander-Reiten theory. We will use the language of category theory throughout the course.
We will mainly follow my book [1]. Other references are [2, 3, 4].
1. Schiffler, Ralf. “Quiver representations”. CMS Books in Mathematics. Springer 2014.
2. Auslander, Maurice; Reiten, Idun; Smalo, Sverre. “Representation theory of Artin algebras”. Cambridge studies in advanced mathematics 36.
3. Crawley-Boevey, William. “Lectures on representations of quivers”. Available on the author’s webpage: https://www.math.uni-bielefeld.de/~wcrawley/ #preprints
4. Assem, Ibrahim; Simson, Daniel; Skowronki. “Elements of the representaiton theory of associative algebras 1: techiques of representation theory”. London Mathematical Society. Student texts 65.
Title: Reading course on Nakajima quiver varieties
Lecturers: Giovanni Cerulli Irelli, Corrado De Concini
Duration: 16 hrs, 2 CFU
Period: from November 15th, Wednesday from 3:30pm to 5:30pm, room B, Dipartimento di Matematica G. Castelnuovo
Abstract: This is a 16 hours reading course on Nakajima quiver varieties. Lectures will be given both by teachers and by interested participants. The material can be asked to Prof. Giovanni Cerulli Irelli by email at giovanni.cerulliirelli@uniroma1.it
Title: Irregular vector fields and divergence theorem
Lecturer: Virginia De Cicco
Duration: 30 ore (4 CFU)
Period: from 09/01/2024, Tuesday, 10:30-12:30, room 1B (RM002)
Abstract: Starting from the classical theory of regular fields, we intend to introduce the Gauss-Green formulas and the Divergence Theorem in increasingly irregular contexts, up to some current research results. After having introduced some basic notions of geometric measure theory, we intend to briefly illustrate the theory of functions of bounded variation and the theory of perimeters. Finally, we aim to define Anzellotti’s pairing between vector fields with measure divergence and BV functions and present its several applications.
Title: A crash course on regularity theory for elliptic PDEs: when coefficients get rough
Lecturer: Stefano Buccheri (Louvain University)
Duration: 20 hrs (3 CFU)
Period: 2 may 2024 16-18 Room 1B (Pal. RM002),
3 may 2024 11-13 Room 1B,
9 may 2024 16-18 Room 1B,
10 may 2024 11-13 Room 1B,
16 may 2024 16-18 Room 1B,
17 may 2024 11-13 Room 1B,
23 may 2024 16-18 Room 1B,
24 may 2024 11-13 Room 1B,
30 may 2024 16-18 Room 1B,
31 may 2024 11-13 Room 1B.
Abstract: (i) A powerful tool in regularity theory for PDEs is given by representation formulas: your solution is expressed by the convolution of the data of the equation with a kernel with known (good) properties. Regularity properties are therefore deduced by such an "explicit" formula. However, if the coefficients of the considered differential operator are not smooth enough, such an approach may fail. (ii) An alternative is provided by a test-function based strategy, that provides the decay of some integral quantities related to truncations of the solution, that in turn is connected with its regularity. (iii) Combining this idea with Steiner symmetrization, one can obtain pointwise estimates on the decreasing rearrangement of both the solution and its gradient. As a by-product of these estimates one can obtain sharp results for the summability of the solution in Lorentz spaces and more in general in rearrangement invariant spaces.
In the course we will recall some classical results connected to (i) for the Poisson equation, apply the strategies outlined in (ii) and (iii) to a large class of equations in divergence form and merely measurable coefficients, and finally try to generalise the obtained results for nonlocal operators.
* Useful courses from undergraduate programmes
Title: Metodi Numerici per l'Ingegneria Biomedica (in Italian)
Lecturer: Francesca Pitolli (SBAI, Sapienza)
Duration: 3 CFU (first part) + 3 CFU (second part)
Period 2023: 26/09-07/11/2023 (first part), 09/11-19/12/2023 (second part), Tue 9:00-11:00 Aula 25 RM031, Thu 15:00-18:00 Aula 41 RM041
Period 2024: First semester (details within the beginning of the semester)
Abstract: Prima parte: Metodi numerici per la soluzione di problemi differenziali, metodi di Runge-Kutta, metodi alle differenze finite (3CFU).
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 (3CFU).
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: ELECTROMAGNETISM
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* Ph.D. courses
Title: Analytical Techniques for Wave Phenomena
Lecturer: Paolo Burghignoli (Sapienza)
Duration: 36 hrs (5 CFU)
Period 2023: 19 September – 26 October, 2023 - Seminar room, second floor of DIET Department - Tuesday 10:00-13:00, Thursday 10:00-13:00
Period 2024: September-October 2024
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: Nanophotonics and Plasmonics
Lecturer: Concita Sibilia (Sapienza)
Duration: 20 hrs, 3 CFU
Period: second semester, Mon and Wed 10:00-12:00, SBAI reading room, RM009 - please contact concita.sibilia@uniroma1.it
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.
Title: Basics of Nonlinear Optics
Lecturer: Concita Sibilia (Sapienza)
Duration: 20 hrs, 3 CFU
Period: second semester, Mon and Wed 10:00-12:00, SBAI reading room, RM009 - please contact concita.sibilia@uniroma1.it
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.
Title: Introduction to Optical Spectroscopic Techniques and Applications to Low Dimensional Semiconductors
Lecturer: Elena Stellino (Sapienza)
Duration: 30 hrs
Period: October 2024
mer 02/10 - 9.00-11.00
ven 04/10 - 9.00-11.00
lun 07/10 - 9.00-11.00
mer 09/10 - 9.00-11.00
ven 11/10 - 9.00-11.00
lun 21/10 - 9.00-11.00
mer 23/10 - 9.00-11.00
Aula 1E, RM004, Via Scarpa 16
Abstract: We will 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 lead s the students to handle real experimental cases. The key objectives 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 software s for the data analysis.
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.
* Useful courses from Master and undergraduate programmes
Title: Thermal Radiation and Infrared Signature
Lecturer: Roberto Li Voti (Sapienza)
Duration: 3 CFU
Period: Online, https://meet.google.com/hdg-gijh-gaz, Wed 17:30-20:00, from 17/01/2024 to 20/03/2024
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.
Title: Laboratory for Industrial Applications of Photothermal and Photoacoustic Optical Technologies
Lecturer: Roberto Li Voti (Sapienza)
Duration: 3 CFU
Period: Fri 10:00-13:00, Room A3, Via Ariosto (Facoltà I3S), from 01/03/2024 to 31/05/2024
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.
Title: Optics
Lecturer: Eugenio Fazio
Duration: 6 CFU
Period: Room 17, ICI San Pietro in Vincoli, Wed 15:00-17:00 and Thu 10:00-13:00
Abstract: https://corsidilaurea.uniroma1.it/en/view-course-details/2023/32384/20190322090929/b11487b2-73a1-4c99-a3cc-2028e7f41e1a/9f2cf951-1b4b-4f0e-8789-9962791dee1b/0823b198-fe5e-4797-a86d-56da889c58c2/3a953bb2-bb39-47d5-9c49-053336965a36
Title: Molecular dynamics and atomistic simulations
Lecturer: Giuseppe Zollo
Duration: 3+3 CFU: Statistical physics and Monte Carlo Techniques (3 cfu), Molecular Dynamics (3 cfu)
Period 2023: First Semester, Room 45, ICI venue S. Pietro in Vincoli, Tue 14.00-17.00, Thu 14.00-16.00
Period 2024: First semester, ICI venue S. Pietro in Vincoli, Room 2 Thu 14:00-17:00, Room 3 Fri 17:00-19:00
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.
Title: Laser Fundamentals
Lecturer: Concita Sibilia
Duration: 6 CFU
Period: Second semester, Tue and Thu 10:30 -13:00, Aula seminari SBAI, RM004
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.
Title: Quantum Information, I
Lecturer: Fabio Bovino
Duration: 5 CFU
Period: First semester, Tue and Thu 17:30-19:45, online (please contact fabioantonio.bovino@uniroma1.it for details)
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.
Title: Quantum Information, II
Lecturer: Fabio Bovino
Duration: 5 CFU
Period: Second semester, Tue and Thu 17:30-19:45, online (please contact fabioantonio.bovino@uniroma1.it for details)
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.
Title: Laboratory experiences for Optics
Lecturer: Alessandro Belardini
Duration: 2 CFU
Period: 14, 21, and 28 June 2024, 17:00-19:45, Building RM008 Floor PS1 Room L013
Title: Advanced Electromagnetics and Scattering
Lecturer: Fabrizio Frezza
Duration: 6 CFU
Period: Second semester, Faculty of Engineering, via Eudossiana 18; Thu 17:00-19:00 room 37; Fri 14:00-17:00 room 20
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.
Title: Microwaves
Lecturers: Marta Cavagnaro (Sapienza), Fabrizio Frezza (Sapienza)
Duration: 9 CFU
Period 2023: First semester, Faculty of Engineering, building RM031; Mon and Tue 10:00-12:00 room 23, Wed 14:00-16:00 room 23 and Thu 14:00-16:00 room 48
Period 2024: First semester, Faculty of Engineering, building RM031; Mon and Tue 10:00-12:00 room 23, Wed 14:00-16:00 room 23 and Thu 14:00-16:00 room 48
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.
Title: Artificial materials, metamaterials and plasmonics for electromagnetic applications
Lecturer: Fabrizio Frezza (Sapienza)
Duration: 6 CFU
Period 2023: First semester, Faculty of Engineering, building RM031, Room 17, Tue 16:00-19:00 and Room 4, Thu 10:00-12:00
Period 2024: First semester, Faculty of Engineering, building RM031, Room 17, Tue 16:00-19:00 and Room 4, Thu 10:00-12:00
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.
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CURRICULUM: MATERIALS SCIENCE
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* Ph.D. courses
Title: Radiation-Matter Interaction, Photoemission and Photoabsorption Spectroscopy, I module
Lecturers: Carlo Mariani, Settimio Mobilio, Francesco Offi, Alessandro Ruocco
Duration: 20 hours, 3 CFU
Period: February-March 2024, precise info by the beginning of the semester
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.
Title: Radiation-Matter Interaction, Photoemission and Photoabsorption Spectroscopy, II module
Lecturers: Carlo Mariani, Settimio Mobilio, Francesco Offi, Alessandro Ruocco
Duration: 20 hours, 3 CFU
Period: April-May 2024, precise info by the beginning of the semester at https://elearning.uniroma1.it/course/view.php?id=5814
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.
* Useful courses from undergraduate programmes:
Title: Surface Physics and Nanostructures (Corso di Laurea in Fisica)
Lecturer: Carlo Mariani (Sapienza)
Duration: 6 CFU
Period 2023: 09-12/2023, Physics Department, Tue 14:00-16:00 room 4, Wed 8:00-10:00 aula Rasetti, Fri 15:00-16:00 aula Careri
Period 2024: 09-12/2024, details within the beginning of the 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, ...).
Title: Chimica Fisica dello Stato Solido e dei Materiali Nanostrutturati (Corso di Laurea in Chimica Industriale, in Italian)
Lecturer: Danilo Dini (Sapienza)
Duration: 6 CFU
Period: Primo semestre, Mer 9:00-11:00 Aula V CU032, Ven 11:00-13:00 Aula V CU032
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.
Title: Sistemi di produzione ed accumulo dell'energia (Corso di Laurea in Chimica Industriale, in Italian)
Lecturer: Maria Assunta Navarra (Sapienza)
Duration: 9 CFU
Period 2023: - Primo semestre, aula D, CU014, LUN 9:00-11:00, MART 9:00-11:00, MERC 11:00-13:00, aula D
Period 2024: Primo semestre, CU014, LUN 11:00-13:00 e MAR 11:00-13:00 aula G, MER 09:00-11:00 aula B
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
Title: Laboratorio Macromolecole (Corso di Laurea in Chimica Industriale, in Italian)
Lecturer: Andrea Martinelli (sapienza)
Duration: 9 CFU
Period: Second semester, Mon, Wed, and Thu, 9:00-11:00, room D, CU014
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.
Title: Microscopies and nanocharacterization techniques
Lecturer: Marco Rossi (Sapienza)
Duration: 9 CFU
Period: Second semester, Mon, Tue, Wed, and Fri 08:00 -10:00 room 17, RM031 (Via Eudossiana)
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.
Title: Chimica e caratterizzazione dei materiali polimerici (Corso di Laurea in Chimica Analitica)
Lecturer: Ilaria Fratoddi (Sapienza)
Duration: 6 CFU
Period: Secondo semestre, aula C, CU035, Mer 12:00-14:00, Gio 13:00-15:00
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: Room 3, ICI San Pietro in Vincoli, Fri 11:00-14:00