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Students


Doctoral theses.



Bachelor theses.


Courses at Universitat Politècnica de Catalunya


2025/2026

Funcions de Variable Complexa at the Facultat de Matemàtiques i Estadística .

Since 2024/2025.


Matemáticas II at the Facultat d'Informàtica de Barcelona.

Since 2023/2024.


Fonaments Matemàtics at the Facultat d'Informàtica de Barcelona .

Since 2024/2025.

2024/2025

Funcions de Variable Complexa at the Facultat de Matemàtiques i Estadística .

This is a first course in complex analysis for bachelor students in Mathematics. The program starts gently with a recall of the topological and algebraic properties of the complex numbers, and then move to the study of functions of one complex variable. In particular, holomorphic functions with their "miracle properties" coming from Cauchy's theorem and Cauchy's formula are studied. The course ends with a brief consideration of meromorphic functions and conformal mappings.


Matemáticas II at the Facultat d'Informàtica de Barcelona.

Since 2023/2024.


Fonaments Matemàtics at the Facultat d'Informàtica de Barcelona .

This is the first course in Mathematics for bachelor students in Informatics Engineering. The program is meant to develop a familiarity with the fundamental mathematical tools that will be needed in the following semesters, starting with the rudiments of logic, the structure of proofs (with a stress on induction), the basic definitions and operations with sets, relations and functions. Finally, some topics from integer numbers are treated: divisibility, primality, euclidean division and modular arithmetics (including the Chinese reminder theorem), together with their applications to the RSA cryptographic system.


Introducció al càlcul at the Grau en Estadística (interuniversitari UB-UPC).

This is a course for first year bachelor students in Statistics. The program involves five main themes, common to most Calculus courses: real numbers, sequences and limits, continuous functions, derivatives and Taylor polynomials, integrals.

2023/2024

Matemáticas II at the Facultat d'Informàtica de Barcelona.

This is a first year bachelor course in Calculus for students in Informatics Engineering. The program starts with the presentation of the notion of real numbers and sequences of those. Then, it dives into the study of the theory of univariate functions, including their derivatives, Taylor polynomials and integrals. Finally, it approaches the world of multivariate functions, with the objective of giving the students necessary tools to compute their extremal points.


Estadística Aplicada.

This is a course for second year bachelor students in Architectural Technology and Building Construction. The program involves five main themes: exploratory data analysis, discrete random variables, continuous random variables, statistical inference and linear models. All treated themes involve the use of the statistical software Minitab.

Courses at Universität Regensburg


2022/2023

Tropical geometry.

The goal of these lectures is to introduce students to the main actors of tropical geometry and to show some applications of the theory.
The course starts by giving some motivating topics from where the subject has found inspiration and source (shortest path in a weighted directed graph, plane tropical curves, enumerative problems and amoebas), and then moves to the presentation of two central results: the Fundamental Theorem of Tropical Geometry and the Structure Theorem for tropical varieties as balanced polyhedral complexes. In doing this, topics like valuations, Newton polytopes, initial forms and Gröbner bases for ideals are needed.
Finally, some applications of the theory are explored: stable intersection of tropical varieties with its application to root counting, connections to toric geometry and to matroids. The course concludes with an overview of a very recent paper by Adiprasito, Huh and Katz, which proves a conjecture on the log-concavity of the coefficients of the characteristic polynomial of a matroid.


Analysis III für Physiker.

I act as teaching assistant for this course, destined to students of the third year of their bachelor in Physics. The lectures, given by Walter Gubler, span across different fundamental topics in Analysis which have important application to Physics: Riemann-integration in several variables, the theory of holomorphic functions and applications to certain partial differential equations.

2021/2022

Toric geometry.

This course aims at giving master students an introduction to the realm of toric varieties, insisting on their consecreted role as a bridge between algebraic geometry and combinatorics. Starting from the development of a vocabulary in the convex world, we make use of it to construct toric varieties and interpret their algebro-geometric properties in terms of the associated combinatorial data.
The course concludes with some ideas of how to apply sheaf cohomology on toric varieties to the theory of Ehrhart polynomials.
During the semester, we also mention some other spectacular applications of toric geometry, such as the Bernstein-Kushnirenko theorem predicting the number of solutions of a system of polynomial equations, and the solution of McMullen's conjecture by Stanley characterizing the collection of integer numbers appearing as the number of faces of a simplicial polytope.

2020/2021

Local class field theory (seminar).

This seminar, organised by Walter Gubler, is intended to late bachelor or early master students having interests in number theory and cohomological methods. The upshots are the computations of the Brauer group of a local field and of the maximal abelian extension of Qp. To get these final results, we introduce the terminology of group cohomology and adopt throughout the approach presented in the book Local Fields by Serre. During our journey, we encounter the Tate-Nakayama theorem on the cohomology of a finite group, Galois cohomology, class formations and local symbols. As tutor for this seminar, I discuss with the students about mathematical questions, I read preliminary versions of their summaries and give them detailed feedbacks.

2019/2020

Elliptic curves (seminar).
The aim of this seminar, managed by Walter Gubler, is to introduce master students to the geometry of elliptic curves. Following the classical book by Silverman The Arithmetic of Elliptic Curves, the talks range from the presentation of these objects via Weierstrass equations to the study of their isogenies, their Tate module and the Weil pairing, concluding with a glimpse towards their geometric study over the field of complex numbers and over local fields. As tutor for this seminar, I am happily available to discuss with the students to clarify questions and to help them preparing their talks; however, due to the current health restrictions, I can only propose virtual meetings via Zoom. Here are some helpful documents related to the seminar:

Courses at Université de Bordeaux


2018/2019

Algèbre bilinéaire et géométrie.

This is a course for second year bachelor students in Mathematics and Engineering mathematics. The program covers the theory of bilinear forms, quadratic forms and scalar products defined over a vector space (with special attention to the finite dimensional case). Some material of the course, as well as some past exams can be found on Laurent Bessières webpage.


Analyse at the Cycle préparatoire de Bordeaux.

The course is given to selected students willing to be admitted to an École d'ingénieurs in the Bordeaux area. The topics treated include the differential calculus of vector-valued functions, the theory of Riemann integrals and improper integrals. Here are some documents related to the course and inspired by Vincent Bruneau's notes:

2017/2018

Bases mathématiques pour les sciences.

The course is meant to give to a heterogeneous audience of first year students the mathematical tools which are necessary in any scientific bachelor degree: rudiments of logic, set theory, basic linear algebra, notions of real and complex numbers, calculus in one real variable and examples of differential equations.


Coloration mathématique.

The course is aimed at first year students willing to pursue a degree in Mathematics. The studied topics (which include sequences of real numbers, functions between sets and equivalence relations) are then treated in details and completeness of proofs.


Mathématiques pour la Biologie.

The goal of the course is to get the students familiar with differential calculus in one variable. The program includes the treatment of continuity, derivation and integration of a real function, Taylor expansion and notions of differential equations. Here are complementary documents to the classes, such as exercise sheets and tables:
Outils Mathématiques pour la Biologie.

This course is the natural continuation of Mathématiques pour la Biologie. The program includes differential calculus in several real variables and the solution of systems of linear differential equations of order one via linear algebra.