Powered by Flash Web Templates Designed by Website Template

I have followed the certification course Flipped Learning 3.0 Higher Education by the Flipped Learning Global Initiave, a coalition of experts from 49 countries. I have implemented this methodology, j.w. W. Pitsch, in a course on Differentiable Manifolds at UAB.

I organized a Summer course on generalized geometry for last-year undergraduate students. It took place between 8th and 19th of July 2019 at the campus of UAB, Barcelona. Participation in the course was through a grant covering travel and accommodation costs.

In 2013 I followed the Teaching Fellowship Preparation programme of the Oxford Learning Institute to become, in 2014, a Fellow of the UK Higher Education Academy (AdvanceHE). Teaching portfolio: ''Climbing mountains together (empathic communication as a teaching philosophy in higher education mathematics)''.

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, enter:

http://mat.uab.es/~rubio/gengeo/


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, enter:

http://mat.uab.es/~rubio/sughib/


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:

generalizedgeometry.blogspot.com


During the four years I spent in Oxford I acted as a teaching assistant and class tutor for departmental teaching, and as a college tutor for several colleges and many subjects. You can see all of them below.


Class tutor at the Mathematical Institute.

B9b Algebraic Number Theory, Hilary 2013.

C3.1b Differentiable manifolds, Hilary 2012.

C2.1a: Lie Algebras, Michaelmas 2011.


College tutor at Jesus College as a Retained Lecturer.

Analysis III, Trinity 2013.

Analysis II, Integration, Group theory, Hilary 2013.


Teaching assistant at the Mathematical Institute.

B9b: Algebraic Number theory, Hilary 2011.

B3a: Geometry of Surfaces, Michaelmas 2010.

C2.1a: Lie Algebras, Michaelmas 2010.

C3.1a: Algebraic Geometry, Michaelmas 2010.


College tutor for other colleges.

Multivariable Calculus, Jesus College, St Hugh’s College, Merton College, Trinity 2013.

Integration, New College, Hilary 2013.

Part A: Multivariable calculus, New College, Merton College, Trinity 2012.

Part A: Integration (revision sessions), St Hugh's College, Trinity 2012.


Other teaching.

College tutor for international students, Lie Algebras (OPUS) and Precalculus (WISC), New College, Hilary 2014.

Tutor in Pure Mathematics for Harlech scholar (Harvard University), New College, Michaelmas 2012, Hilary and Trinity 2013.

College tutor for international students, Prelims Multivariable Calculus, New College, Hilary 2013.

Elements of Real Analysis (Mods Analysis I, Analysis II and Analysis III). Tutor for international students. New College, Michaelmas 2011.

2003-2010 Trainer of the Valencian team for the Spanish Mathematical Olympiad.

2004-05 Foundations of Mathematics, class tutor (estudiante tutor).

2003-04 Foundations of Mathematics, class tutor (estudiante tutor).

Upcoming and latest

Rear window
Contact Info