| Elenco delle attività formative previste per i dottorandi del secondo anno |
Spectral Geometry
data presunta: 03-05/2025 - tipologia: riconducibile al progetto formativo - modalità di erogazione: Ex-cathedra - numero ore: 24
docente del corso: Luigi Provenzano (Sapienza) e Davide Buoso (U. Piemonte Orientale) qualifica: Professore affiliazione: Italiana
programma delle attività: In the first part of the course we will provide a brief introduction to the spectrum of the Laplacian on Euclidean domains and Riemannian manifolds, along with a few basic examples, and their relations with physical phenomena (waves and vibrations).
Then, we will focus on some classical problems in spectral geometry, such as eigenvalue bounds and isoperimetric inequalities for the eigenvalues. The questions that we will address are the following: how does the geometry and the topology of the ambient space influence the spectrum (the eigenvalues)? On the other hand, what information can give the knowledge of the spectrum on the geometry and topology of the ambient space?
We will present a few classical techniques which have been adopted throughout the years to address these questions. In the final part of the course (if time allows) we will consider some recent developments on old and new problems, and we will present some open questions.
modalità di accertamento finale: Short seminar/report on a research paper (possibly close to the student's interests)
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Radiation-Matter Interaction, Photoemission and Photoabsorption Spectroscopy, I
data presunta: 02-03/2025 - tipologia: riconducibile al progetto formativo - modalità di erogazione: Ex-cathedra - numero ore: 20
docente del corso: Carlo MARIANI (PO Sapienza), Settimio MOBILIO (emerito, Roma Tre), Francesco OFFI (PA, Roma Tre), Alessandro RUOCCO (PA, Roma Tre) qualifica: Professore affiliazione: Italiana
programma delle attività: 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.
modalità di accertamento finale: oral presentation of a current research topic which uses the methods presented in the course..
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Radiation-Matter Interaction, Photoemission and Photoabsorption Spectroscopy, II
data presunta: 04-05/2025 - tipologia: riconducibile al progetto formativo - modalità di erogazione: Ex-cathedra - numero ore: 20
docente del corso: Carlo MARIANI (PO Sapienza), Settimio MOBILIO (emerito, Roma Tre), Francesco OFFI (PA, Roma Tre), Alessandro RUOCCO (PA, Roma Tre) qualifica: Professore affiliazione: Italiana
programma delle attività: 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.
modalità di accertamento finale: oral presentation of a current research topic which uses the methods presented in the course.
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Advances in Raman spectroscopy: from traditional vibrational spectroscopy to surface enhanced approaches
data presunta: 04-05/2025 - tipologia: riconducibile al progetto formativo - modalità di erogazione: Ex-cathedra - numero ore: 10
docente del corso: Angela CAPOCEFALO qualifica: Ricercatore affiliazione: Italiana
programma delle attività: 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.
modalità di accertamento finale: oral presentation of a current research topic which uses the methods presented in the course.
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Neural Networks & Machine Learning
data presunta: 01-02/2025 - tipologia: riconducibile al progetto formativo - modalità di erogazione: Ex-cathedra - numero ore: 30
docente del corso: Adriano Barra qualifica: Professore affiliazione: Italiana
programma delle attività: The course is meant to provide theoretical tools (both mathematical and computational) to allow the students to orient themselves in the proliferation of neural network techniques and machine learning algorithms that are nowadays broadly used in the processing of data and signals both in the world of research as well as in industry. Specifically, once shared the main mathematical methodological bases (a quick review of elements of probability and statistics), after a succinct historical introduction (e.g. the Turing machine, Rosenblatt's perceptron and AI’s winter time), modern neural networks will be addressed, both those biologically inspired (e.g. the Hopfield model and its variations on the theme) as well as those not-biologically inspired (Boltzmann machines and feed-forward networks), with the related algorithms for learning and automatic recognition (e.g., contrastive divergence and back -prograpation). The ultimate aim of the course is to share the salient concepts with the students and, at the same time, to provide them with the key tools, so that they can keep growing within the field of Artificial Intelligence and Machine Learning: this transfer of information will be supplied both from a formal/mathematical point of view (e.g. showing during the course clear methods for setting up a relevant problem and solving it appropriately) and from a logical/deductive point of view (e.g. understanding what it is reasonable to be addressed by modern techniques of Machine Learning).
To this end the course program is divided into two main sections. The former is to ensure that we share basic scientific knowledge (obviously a necessary pre-requisite to guarantee that we understand information processing in neural networks from a mathematical perspective later on). The latter is completely dedicated to neural networks: after a succinct description (always in mathematical terms) of the key mechanisms inherent to the neuron and the propagation of information between neurons, "networks of neurons" will be built (in other words they will explain " what are” -mathematically speaking- these neural networks) and we will study their emergent properties (i.e. those not immediately deducible by looking at the behavior of the single neuron): specifically, we will try to see how these networks are able to learn and abstract by looking at supplied examples from the external world and how, subsequently, they use what they have learned to respond appropriately, if stimulated, to the external world. We will also understand how these neural networks can sometimes make mistakes, and why. Ideally at the end of the course the students should be able to independently continue in-depth study of this discipline and benefit from it accordingly during their careers
modalità di accertamento finale: Oral exam
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Advances in Raman spectroscopy: from traditional vibrational spectroscopy to surface enhanced approaches
data presunta: 04-05/2025 - tipologia: riconducibile al progetto formativo - modalità di erogazione: Ex-cathedra - numero ore: 30
docente del corso: Elena Stellino qualifica: Ricercatore affiliazione: Italiana
programma delle attività: The course is meant to provide theoretical tools (both mathematical and computational) to allow the students to orient themselves in the proliferation of neural network techniques and machine learning algorithms that are nowadays broadly used in the processing of data and signals both in the world of research as well as in industry. Specifically, once shared the main mathematical methodological bases (a quick review of elements of probability and statistics), after a succinct historical introduction (e.g. the Turing machine, Rosenblatt's perceptron and AI’s winter time), modern neural networks will be addressed, both those biologically inspired (e.g. the Hopfield model and its variations on the theme) as well as those not-biologically inspired (Boltzmann machines and feed-forward networks), with the related algorithms for learning and automatic recognition (e.g., contrastive divergence and back -prograpation). The ultimate aim of the course is to share the salient concepts with the students and, at the same time, to provide them with the key tools, so that they can keep growing within the field of Artificial Intelligence and Machine Learning: this transfer of information will be supplied both from a formal/mathematical point of view (e.g. showing during the course clear methods for setting up a relevant problem and solving it appropriately) and from a logical/deductive point of view (e.g. understanding what it is reasonable to be addressed by modern techniques of Machine Learning).
To this end the course program is divided into two main sections. The former is to ensure that we share basic scientific knowledge (obviously a necessary pre-requisite to guarantee that we understand information processing in neural networks from a mathematical perspective later on). The latter is completely dedicated to neural networks: after a succinct description (always in mathematical terms) of the key mechanisms inherent to the neuron and the propagation of information between neurons, "networks of neurons" will be built (in other words they will explain " what are” -mathematically speaking- these neural networks) and we will study their emergent properties (i.e. those not immediately deducible by looking at the behavior of the single neuron): specifically, we will try to see how these networks are able to learn and abstract by looking at supplied examples from the external world and how, subsequently, they use what they have learned to respond appropriately, if stimulated, to the external world. We will also understand how these neural networks can sometimes make mistakes, and why. Ideally at the end of the course the students should be able to independently continue in-depth study of this discipline and benefit from it accordingly during their careers.
modalità di accertamento finale: Students, organized into groups, must prepare written reports for each teaching module detailing the laboratory experience, scientific case, experimental setup, data analysis, and result interpretation. At the course's conclusion, each student must present and discuss a scientific article from the literature that utilizes one of the discussed techniques. Evaluation will be based on three group reports and one individual presentation, resulting in a grade from 0 to 30. The final mark is an average of these four scores.
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On the Dirichlet problem for elliptic equations with rough data
data presunta: 04-05/2025 - tipologia: riconducibile al progetto formativo - modalità di erogazione: Ex-cathedra - numero ore: 20
docente del corso: Francescantonio Oliva qualifica: Ricercatore affiliazione: Italiana
programma delle attività: We will first consider Dirichlet problems associated to elliptic equations whose principal operator is in divergence form with bounded coefficients. We briefly present the weak setting for these equations with a measurable function f belonging to a suitable Lebesgue space or even a Radon measure as a source datum. In accordance with the regularity of f we introduce the concept of weak, distributional and renormalized solution and we prove their well-posedness.
In the second part, we deal with source terms of the form f(x)h(u) which can also depend on the solution u itself. We deal with the case of a function h(s) which has a finite limit at infinity, continuous and possibly blowing up at the s=0; as a prototypical example one should have in mind a negative power. For these equations we show existence, regularity, and uniqueness of finite and infinite energy solutions. If the time allows, we could also deal with the case of equations involving first order terms with natural growth with respect to the gradient.
Depending on the attendees background knowledge, the course will mainly focus on the first and/or the second part.
modalità di accertamento finale: Seminar
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An introduction to cluster algebras
data presunta: 03-04/2025 - tipologia: riconducibile al progetto formativo - modalità di erogazione: Ex-cathedra - numero ore: 16
docente del corso: Giovanni Cerulli Irelli qualifica: Professore affiliazione: Italiana
programma delle attività: We review the theory of cluster algebras intiated by Fomin and Zelevinsky in 2001 and its connection with the rapresentation theory of associative algebras, following Derksen, Weyman and Zelevinsky.
modalità di accertamento finale: Seminar
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Analytical Techniques for Wave Phenomena
data presunta: 09-10/2025 - tipologia: riconducibile al progetto formativo - modalità di erogazione: Ex-cathedra - numero ore: 36
docente del corso: Paolo Burghignoli qualifica: Professore affiliazione: Italiana
programma delle attività: 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.
modalità di accertamento finale: Oral discussion of course's topics.
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Nanophotonics and Plasmonics
data presunta: 03-04/2025 - tipologia: riconducibile al progetto formativo - modalità di erogazione: Ex-cathedra - numero ore: 20
docente del corso: Concita Sibilia qualifica: Professore affiliazione: Italiana
programma delle attività: 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.
modalità di accertamento finale: Oral discussion of course's topics.
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Basics of Nonlinear Optics
data presunta: 04-05/2025 - tipologia: riconducibile al progetto formativo - modalità di erogazione: Ex-cathedra - numero ore: 20
docente del corso: Concita Sibilia qualifica: Professore affiliazione: Italiana
programma delle attività: 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.
modalità di accertamento finale: Oral discussion of course's topics.
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Experiences in Optics
data presunta: 11/2024-02/2025 - tipologia: riconducibile al progetto formativo - modalità di erogazione: Ex-cathedra - numero ore: 20
docente del corso: Alessandro Belardini qualifica: Professore affiliazione: Italiana
programma delle attività: 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.
modalità di accertamento finale: Oral discussion of course's topics.
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