# Tentative schedule for the courses of the XXXVI cycle

The following courses are planned for the first two years of the cycle. The precise dates will be made available at the beginning of the academic year 2020-2021 (the course is still under evaluation for accreditation).

### Math and Computer Science Courses

**Optimization models for Machine Learning**, Prof. Antonio Fuduli, 4CFU*Abstract.*During the course some optimization models applied to the classification of data will be presented, with particular regard to the binary case. A distinction will be made between the supervised, unsupervised and semi-supervised case and some concepts related to the problems of Multiple Instance Learning will be introduced.

**Elements of Algebraic Geometry**, Prof. Francesco Polizzi, 4CFU*Abstract.*Topics of the course include: Eilenberg-Steenroad axioms and their consequences, Singular homology, Topological degree theory, CW-complexes and cell maps, Succession of Mayer-Vietoris, Geometric consequences: the Jordan curve theorem, the Borsuk-Ulam theorem, the Lefschetz-Hopf fixed point theorem.

**Multivariate interpolation methods**, Prof. Francesco Dell'Accio, 4CF*Abstract.*The problem of determining a continuous function of several variables, given a finite set of observations, has attracted the attention of a large group of researchers since the second half of the last century. With the advent of modern computers, the topic has become of great interest, both theoretical and practical, due to the charm of the buildings and the numerous application implications. Interpolation using polynomials, in particular, has received constant attention from the mathematical community, and is currently one of the basic topics of the interpolation theory in several variables. The course aims to introduce basic techniques, also indicating applications to the difficult case of scattered data, which is one of the hot research topics of approximation theory.

**Social Network Analysis**, Prof. Gianluigi Greco, 4CFU*Abstract.*The years following the emergence of the web can be seen as the years of the social computing. Several social applications appeared, such as facebook and twitter. Technological and economical systems we use in our everyday life are based on extremely complex networks and it is getting more and more difficult to understand how these systems work. To deal with these new systems we have to change our paradigm and learn to reason about an highly interconnected world. It is of fundamental importance to be able to understand how these networks work and recognize and control the processes that develop in a network. This course aims to give students the tools to better understand and control highly connected networks, with particular emphasis to social and information networks technologically mediated.

**Introduction to continuous time Markov processes and applications**, Prof. Michele Gianfelice, 4CFU*Abstract.*The aim of the course is to introduce the audience to the study of a cornerstone of the theory of stochastic processes which is the theory of Markov processes. Markov processes are ubiquitous in applications: from physics to biology to engeneering. Hence, the applications presented will follow the choice of the audience.

**Introduction to statistical properties of deterministic systems and their random perturbations**, Prof. Michele Gianfelice, 4CFU*Abstract.*The aim of the course is to introduce the audience to the study of the invariant measures of deterministic systems and the properties of the associated stationary processes such as large deviations and central limit theorem as well as their stochastic stability.

**Pythagorean hodograph curves**, Prof. Kai Hormann, 4 CFU*Abstract.*Pythagorean-hodograph curves are characterized by the special property that their “parametric speed” — i.e., the derivative of the arc length with respect to the curve parameter — is a polynomial (or rational) function of the parameter. This distinctive attribute, achieved by a priori construction of the hodograph (derivative) components of polynomial or rational curves in ℝn as elements of Pythagorean (n+1)–tuples, endows the Pythagorean–hodograph (PH) curves with many computationally attractive features. In contrast to the traditional (Bézier/B–spline) schemes of computer-aided geometric design, the PH curves require models that are inherently non-linear in nature. However, by use of appropriate algebraic tools — complex numbers and quaternions for planar and spatial PH curves — their construction and analysis are greatly facilitated. The investigation of PH curves thus offers an excellent context and motivation for exploring the pervasive ties between algebra and geometry.

**Classic algorithms: past, present and future.**, Prof. Annarosa Serpe, 4CFU*Abstract.*Often overlooked by historians and modern scientists, more concerned with the nature of concepts, algorithmic procedures have been instrumental in developing fundamental ideas: practice has led to theory as much as the other way around. The course offers a historical background to algorithmic practice. Specifically, it focuses attention on the structure of Euclid's algorithm which often represents the prototype of the algorithmic procedure for mathematicians and which has relevance to date. Euclid's algorithm can be useful not only in the search for the greatest common divisor - as described by Euclid himself - but also, by adapting the procedure, in the solution of indeterminate equations, which leads to the identity of Bézout. This algorithm allowed al-Khwarizmi (ca 780 - ca 850) to compare two ratios, or to prove that they were the same; all this appears even more clearly in the writing of the continuous fractions which have been systematically studied by Euler. Finally, (it may seem surprising) the algorithm can be used in the Sturm method to determine the number of real roots of an algebraic equation.

**Nonlocal Elliptic PDEs**, Prof. Luigi Montoro, 4CFU*Abstract.*Recently great attention has been focused to the study of elliptic equations involving the fractional laplacian operator that arises in many applications. Motivated by this increasing interest, this course deals with an introduction to some classical arguments used in the nonlocal framework and to some classes of nonlocal problems.

**Lecture in Nonlinear Analysis and Differential Equations - Part I**, Prof. Gennaro Infante, 4CFU*Abstract.*The course will feature a number of seminars of different professors on topics related to nonlinear analysis and differential equations. All professors will be visitor of the University of Calabria, under the Erasmus+ programme.

**Lecture in Nonlinear Analysis and Differential Equations - Part II**, Prof. Gennaro Infante, 4CFU*Abstract.*The course will feature a number of seminars of different professors on topics related to nonlinear analysis and differential equations. All professors will be visitor of the University of Calabria, under the Erasmus+ programme.

**Embodiment of AI**, Prof. Elena De Momi, 4CFU*Abstract.*Robots are more and more pervading everyday life, assisting driving and professional activities. In the healthcare sectors, they can assist disabled, improve the rehabilitation pathway and increase the surgical action safety, improving the clinical outcome. The PhD course “Embodiment of AI” aims at providing students with elements of robotics, seeing robots as embodiments for AI tools. In detail, the course will provide an overview on methods for model-based and model-free robotic control tasks and on methods (e.g. based on deep learning) for scene interpretation using environmental camera information. In the second part of the course, planning methodologies will be introduced, such as path planning using reinforcement learning and ontologies for decision process modelling. Hands-on activities will be implemented.

### Other Courses

**Technical English**, 4CFU*Abstract.*Elements of technical English, Writing of scientific papers, speaking and comprehension of presentations, Tool tips on writing a good Ph.D. thesis.

**Research management**, 4CFU- Provided by the Liaison Office of the University of Calabria

**Exploitation of research results**, 4CFU- Provided by the Liaison Office of the University of Calabria