Tentative schedule for the courses of the XXXIX cycle
Rules: Doctoral students are required to achieve a minimum of 24 CFU over three years. Of these CFU, a minimum of 18 CFU must be completed as part of the specialised teaching of their doctorate and a minimum of 6 CFU as transversal or not strictly related teaching. At least 70% of the teaching activity must be carried out within the University Catalogue.
By December of each year, students must present a tentative study plan to the doctoral board. During the examination for passing to the following year, doctoral students must present the committee with a list of the courses they have taken and their certificates of passing the final examination. The doctoral board will approve the teaching plan, distinguishing between specialised and transversal activities and between catalogue and extra-catalogue activities.
The following courses are planned for the first two years of the cycle. The precise dates of the first year courses will be made available at the beginning of the academic year 2023-2024.
Each course includes a final test to certify the knowledge and skills acquired by the students.
Math and Computer Science Courses
Courses Planned for the first year (2023-2024)
Advanced Methods, Tools and Applications for Artificial Intelligence, 3CFU
Abstract. Artificial Intelligence may be described as one of the most important research areas of our time. This course aims to cover the most recent approaches in AI, focusing on innovative methodologies, applications and tools. Since the typical notion of data is usually focused on heterogeneity and is rather dynamic in nature, computer science researchers are encouraged to develop new or adapt existing suitable artificial intelligence models, tools, and applications to effectively solve these problems; as a consequence, this area of research is very active and new methods, tools and applications are continuously available. The exact topics of the course may vary from year to year and will depend on both the research interests of the students attending it and on the instructor.
Traditional and Emerging Methods for High Performance Computing, 3CFU
Abstract. High-performance computing (HPC) is the use of super computers and parallel processing techniques for solving complex computational problems. HPC technology focuses on developing parallel processing algorithms and systems by incorporating both administration and parallel computational techniques. This course covers Traditional and Emerging Methods for HPC. The exact topics of the course may vary from year to year and will depend on both the research interests of the students attending it and on the instructor.
Computer and Data Science Innovation in Multidisciplinary Areas, 3CFU
Abstract. This course offers an advanced training in computer science with particular emphasis on Data Science applications as a multidisciplinary field of study promoting the transversal synergies between scientific and social disciplines. The exact topics of the course may vary from year to year and will depend on both the research interests of the students attending it and on the instructor. Upon completion of this course, the student will have a deeper understanding on some of the latest research problems in one of the areas of data science innovation.
Topics in Algebra, 3CFU
Abstract. The topics of this course cover a wide range of arguments in algebra and include (but are not restricted to): p-adic completions; group theory; representation theory; Groebner bases; elliptic curves; proof techniques; combinatorics. The course contents will vary annually depending on the research interests of the students attending it.
Didactical aspects of Mathematics, 3CFU
Abstract. Study and analysis of the quantitative and qualitative research methods of teaching-learning theory, social and cultural contexts of education, curriculum and instruction theory, assessment, professional development, teacher beliefs, and student attitudes in mathematics education. Specifically, critical analysis of the principal methodologies for teaching developed in research in mathematics education and in history of mathematics, also with reference to conceptual, epistemological, linguistic and didactic nodes of mathematics teaching and learning. The exact topics of the course may vary from year to year and will depend on both the research interests of the students attending it and on the instructor.
Topics in PDEs, 3CFU
Abstract. The course is concerned with the study of linear and nonlinear PDEs and all the correlated issues from functional analysis. In particular we shall focus on existence or nonexistence of solutions, qualitative properties of the solutions and regularity theory. Real world applications will be also discussed. The exact topics of the course may vary from year to year and will depend on both the research interests of the students attending it and on the instructor.
Interpolation and approximation with applications, 3CFU
Abstract. The course aims to discuss advanced topics on both classic and new approaches to interpolation and approximation, mainly polynomial-based but not only, and their applications to the numerical solution of real world problems. The exact topics of the course may vary from year to year and will depend on both the research interests of the students attending it and on the instructor.
Advanced optimization models and methods, 3CFU
Abstract. The main objective of the course is to present and discuss some advanced optimization models, finding application in different practical fields, such as machine learning, logistics, economics, and finance. Part of the course is also devoted to the introduction of recent techniques providing exact and heuristic approaches in operations research and numerical optimization. The exact topics of the course may vary from year to year and will depend on both the research interests of the students attending it and on the instructor.
Additional Planned Courses
Approximate Dynamic Programming for Dynamic Optimization Problems, 3CFU, Ref. Demetrio Laganà
Abstract. Approximate dynamic programming (ADP) has evolved, initially independently, within operations research, computer science and the engineering controls community, all searching for practical tools for solving sequential stochastic optimization problems. More so than other communities, operations research continued to develop the theory behind the basic model introduced by Bellman with discrete states and actions, even while authors as early as Bellman himself recognized its limits due to the “curse of dimensionality” inherent in discrete state spaces. In the operations research community, ADP has been equated with the use of value function approximations which has separated it from the stochastic programming community (a form of lookahead policy) or simulation optimization (which typically involves policy search). The aim of the lectures is to provides a broad overview of approximate dynamic programming.
Courses Planned for the second year (2024-2025)
Advanced Models and Methods for Knowledge Representation and Reasoning, 3CFU
Abstract. Knowledge representation and reasoning (KRR) is the field of artificial intelligence (AI) dedicated to representing information about the world in a form that a computer system can use to solve complex tasks. Knowledge representation and reasoning incorporates findings from logic to automate various kinds of reasoning and from psychology about how humans solve problems and represent knowledge. This course aims to present the most recent advances and state-of-the art models and methods in KRR. The exact topics of the course may vary from year to year and will depend on both the research interests of the students attending it and on the instructor.
Advanced Topics in Theoretical Computer Science, 3CFU
Abstract. This course covers advanced topics in theoretical aspects of computer science. Topics falling under this module include algorithms, theory of computation, formal models, and semantics. The exact topics of the course may vary from year to year and will depend on both the research interests of the students attending it and on the instructor. Upon completion of this course, the student will have a deeper understanding on some of the latest research problems in one of the areas of theoretical computer science.
Advanced Learning Models and Methods , 3CFU
Abstract. Nowadays learning models and methods spans multiple fields in science and engineering, from autonomous driving to human machine interaction, achieving human performance in solving many complex tasks, such as natural language processing and image recognition. This course aims to present the most recent advances in machine and deep learning that brought data-driven models to achieve the state-of-the art performance in many diverse problems. The exact topics of the course may vary from year to year and will depend on both the research interests of the students attending it and on the instructor.
Topics in Differential and Algebraic Geometry, 3CFU
Abstract. The course will focus on deformation theory and classification problems in algebraic geometry, complex geometry and/or differential geometry: classification of real manifolds; Riemann surfaces; moduli spaces of curves (compact Riemann surfaces) of genus g; families of curves in algebraic varieties; deformation theory of singularities of algebraic complex curves and surfaces, etc. The topic of the course may change year by year and it will depend on the research interests of the students attending it.
Topics in Nonlinear Analysis, 3CFU
Abstract. The course is devoted to classical and recent results in nonlinear functional analysis and its applications to differential equations. Particular attention is given to various aspects of the solvability on nonlinear equations in abstract spaces: existence, non-existence, multiplicity and approximability of the solutions. Applications of the abstract results to differential problems is also discussed. The exact topics of the course may vary from year to year and will depend on both the research interests of the students attending it and on the instructor.
Introduction to continuous time Markov processes and applications, 3CFU
Abstract. The aim of the course is to introduce the audience to the theory of continuous time Markov processes (ctMp). After a recap of the basic notions of descrete time random processes such as Markov chains (Mc) and (sub/super)martingale, we will concentrate on Feller processes and discuss jump processes and one-dimensional diffusions. The rest of the course will be devoted to satisfy the interests of the audience. For example, for those interested in the connections between ctMp and PDE, we will discuss example of representations of solutions of parabolic PDE in terms of the Feynmann-Kac formula or of certain nonlinear PDE in terms of superdiffusions, as well as describe weak solutions of such differential equations as diffusive limit of empirical densities of certain ctMp a.k.a. Interacting Particle Systems.
Topics in Mathematical Physics, 3CFU
Abstract. The course will cover topics on: Ordinary differential equations and Mechanical Systems; Reaction-Advection-Diffusion Equations and their applications in Physics, Biology and Chemistry; Hyperbolic Equations and their applications in Rational Extended Thermodynamics; Interpolation and approximation with applications; Optimization models and methods. The exact topics of the course may vary from year to year and will depend on both the research interests of the students attending it and on the instructor.
Transdisciplinary Courses:
Please check the University Catalogue available at https://www.unical.it/didattica/offerta-formativa/dottorati/attivita-didattiche-dei-corsi-di-dottorato/
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