Roberto Rubio

Since July 2022 I hold a research-based position. I am allowed to teach a limited number of hours a year, which I am using to supervise several final-year projects on various topics: geometry, mathematical foundations of machine learning, and music and mathematics.

Geometric structures and generalized geometry. First semester 2021/22. Graduate course.

Scoping review on geometric structures combined with an introduction to generalized geometry. 42 hours. Official information at the Feinberg Graduate School. To access materials through Perusall, click here.

Linear algebra. Second semester 2020/21. 1st-year, problem+lab sessions.

A course on linear algebra: vector spaces, linear maps, dual space, diagonalization of endomorphisms, bilinear forms, Jordan canonical form. For more detailed information, check the syllabus of the course (in Catalan).

Mathematics I, BSc in Chemistry. Second semester 2020/21. 1st-year, theory+problems.

A course covering complex numbers, exponentials and logarithms, diagonalization of matrices, quadratic forms, differential equations and multivariable calculus. For more detailed information, check the syllabus of the course (in Catalan).

Differentiable manifolds. First semester 2020/21. 4th-year, theory+problem sessions.

A course on differential topology. I am in charge, on an equal footing with W. Pitsch, of the course, 50 hours. We are implementing the flipped classroom methodology as an innovation teaching project. For more detailed information, check the syllabus of the course in English.

Current mathematical trends. Annual 2020/21. 4th-year, theory.

A course consisting of seven mini-courses (6h) showing seven recent trends in mathematics. I am in charge of a mini-course about Moduli spaces. The coordinator of this course is Artur Nicolau. For more detailed information, check the syllabus of the course in English.

Linear geometry. First semester 2020/21, 2019/20, 2018/19. 2nd-year, problem sessions.

A course dealing with Euclid and Hilbert's axiomatizations, projective and affine geometry, and quadrics. I am in charge of the problem sessions for one group, 15 hours. The lecturer is Jaumé Aguadé. For more detailed information, check the syllabus of the course in English.

Algebra, BSc in Computer Engineering. First semester 2019/20. 1st year, problem sessions.

An introductory course of linear algebra, focusing on the most functional and instrumental aspects. I am in charge of the problem sessions for one group. Coordinator of the course: Francesc Perera. For more detailed information, check the syllabus of the course in English.

Generalized geometry, an introduction. Second semester 2017/18. Graduate course.

A basic but solid introduction to generalized geometry. 42 hours. Official information at the Feinberg Graduate School. For more detailed and updated information, lecture notes and assignments, click here.

Introduction to surface group representations and Higgs bundles. First semester 2017/18. Graduate course.

A very mild introduction to surface group representations, the definition of a Higgs bundle and the Hitchin-Kobayashi corresponde. 42 hours. Official information at the Feinberg Graduate School. For more information, lecture notes and assignments, click here.

Clifford algebras, spinors and applications. January-February 2017. Graduate course.

A course devoted to understanding and working with spinors from the point of view of Clifford algebras. 48 hours. The problem sheets, a more precise syllabus, a list of the student presentations and the bibliography can be found in this repository.

Tópicos de Geometria Diferencial: Dirac structures and generalized geometry, joint with H. Bursztyn. January-February 2016. Graduate course.

I was in charge of the first half of the course, 24 hours, dealing with the very basics of Dirac structures, Courant algebroids and generalized complex structures. The problem sheets are available in this repository.

Introduction to Generalized Geometry. January-February 2015. Graduate course.

The first time I taught generalized geometry, 48 hours. I kept a weblog the first weeks of the course, where some lecture notes and all the problem sheets can be found, at: