Teaching

Bachelor course Engineering: Linear algebra and analytic geometry

Bachelor course Data Analytics: Linear algebra

Bachelor course Biotechnologies and Environmental science: Calculus [with Giuseppina di Blasio]

Master course Mathematics: Combinatorial geometry and its applications [with Vito Napolitano]

Master course Mathematics: Algebraic geometry [with Olga Polverino]

PhD course: Algebraic and geometric methods in combinatorics and information theory [with Olga Polverino]

In this course we will first explore classical and more recent objects in combinatorics, such as arcs, caps, linear sets and blocking sets, and we will see how to use algebraic and geometric techniques to get more insight on these objects.

The second part will be devoted to developing geometric and algebraic techniques to be applied in communication channels, which will regard linear algebra over finite fields, representation theory, Galois geometries and incidence structures.

PhD course: Computer Algebra Software for Algebraic and Geometric Problems [with Olga Polverno and Paolo Santonastaso]

Computer Algebra Systems (CAS) are powerful tools designed for both symbolic and numerical computations across a wide range of mathematical disciplines. They can handle basic operations in areas like linear algebra or calculus, while also supporting advanced functions for manipulating objects such as groups, graphs, and representations. By using a CAS, mathematicians (and not only) can explore problems by computing examples, testing conjectures, and identifying patterns and structures within the results. In this course, we will introduce SageMath and GAP. SageMath is an open-source mathematics software system with extensive capabilities, built on Python. GAP is specialized for computational discrete algebra, with a particular focus on computational group theory. It offers its own programming language, an extensive library of algebraic algorithms, and vast data libraries of algebraic objects. We will not only learn how to use SageMath and GAP for practical computations but also how to develop new code and even software packages for solving specific algebraic and combinatorial problems.

PhD course: Combinatorics and its applications [with Olga Polverino]

Combinatorics is a branch of Mathematics of increasing importance, owing to its links with Information Theory, Statistics and other areas of Mathematics, such as Algebra and Geometry. This course will be a gentle introduction to the classical combinatorics and the new trends in Galois geometry, then focusing on some new recent aspects and some applications to Coding Theory and to Cryptography.

The topics of the course regard:

●  Linear sets (Projection of subgeometries, Geometric and Algebraic field of linearity)

●  Blocking sets (linear and non-linear, Rédei type, nuclei of pointsets)

●  Applications (Coding Theory and Cryptography)

PhD course: Algebraic and geometric methods in Information Theory

The first part of this course provides an overview on the mathematical measures of information and their connection to practical problems in communication, compression, and inference (within entropy, mutual information, lossless data compression, channel capacity, Gaussian channels, rate distortion theory, Fisher information). This could turn out to be useful for PhD students in mathematics, signal processing, machine learning, statistics, and neuroscience.

The second part will be devoted to developing geometric and algebraic techniques to be applied in communication channels, which will regard linear algebra over finite fields, representation theory, Galois geometries and incidence structures.

Moreover, the last two lectures will be dedicated to some algebra software, such as MAGMA, GAP or SageMath, and the students will elaborate projects on some aspects of the developed theory supported by the use of such softwares.

For more details see link.

References

• Introduction to coding theory, A. Couvreur; 

• Elements of Information Theory, T.M. Cover and J.A. Thomas, John Wiley & Sons 1999;

• Essential Coding Theory, V. Guruswami, A. Rudra and M. Sudan;

• Codes, Cryptology and Curves with Computer Algebra, R. Pellikaan, X.-W. Wu, S. Bulygin and R. Jurrius, Cambridge University Press 2018;

• Coding Theory, A. Ravagnani.

For an algebraic recap see Rings and fields - Lectures by Alexei Skorobogatov, Mathematics Imperial College London 

PhD course: Geometric Techniques in Modern Coding Theory [Université Paris 8]

This course provides an introduction to geometric methods in modern coding theory, with particular emphasis on the interplay between finite projective geometry and linear codes. We will discuss classical geometric configurations such as arcs in projective spaces, their connection with maximum distance separable (MDS) codes, and some of the fundamental structural results governing their existence and classification. Special attention will be devoted to Segre’s theorem on ovals and to some of its consequences in finite geometry and coding theory. The course aims to illustrate how geometric ideas and techniques can be used to understand, construct, and classify codes with extremal properties.