Teaching

Introductory analysis in multiple variables (inleiding analyse in meer variabelen)

I am the lecturer of this course, at the UU, since 2023. The lecture notes for the course can be found here. They were developed originally by Erik van den Ban, and have been updated by me since. The exercise booklet can be found here. Both are in English.

Introduction to algebraic topology (topologie en meetkunde)

I was the lecturer of this course, at the UU, in the period 2019-2023. I developed a set of lecture notes, which you can find here, in English. The idea behind them is threefold: (1) The primary goal is to study the fundamental group; this is done in a somewhat standard manner, as in Hatcher, but we depart from it in many places and generally include more details. (2) The secondary goal is to introduce the language of category theory as it becomes relevant, and to emphasise categorical thinking. (3) The last goal is to tackle the classification of surfaces. The notes will be finalised in the upcoming year.

I have also made short videos covering some of the topics central to the course. You can find them here.

During corona the course was taught remotely. The video recordings can be found here. Note that they do not match the latest version of the notes, and the quality is just okay.

Spring 2025

I taught Calculus and Linear Algebra I at University College Utrecht.

Fall 2022

I taught Topology of geometric structures, a local master course for second year students. The course covered some of the basics of Differential Topology (bordism theory, fibre bundles, jet spaces, Whitney topologies, transversality, triangulations, and a brief look at h-principle).

In the bachelor, I taught Inleiding Analyse in meer variabelen (analysis in multiple variables).

Fall 2021

I taught Bewijzen in de Wiskunde (Proofs in Mathematics), for 1st year students in Mathematics.

BKO portfolio

I obtained the basic teaching qualification (BKO) in 2022. While developing my portfolio I attended the course “Teaching in Higher Education” to work on my teaching/supervising/tutoring.

Spring 2019

I taught the Symplectic Geometry course offered by the Dutch Mastermath programme together with Fabian Ziltener. You can find the course’s website here. You can find additional information about the course on the ELO website.

Fall 2018

We did a reading seminar on the Madsen-Weiss theorem (within the framework of the Friday Fish seminar). The main organiser was Thomas Rot and in his webpage most of the details of the seminar can be found.

Summer 2018

I gave a 4-hour minicourse “A gentle introduction to Morse theory” in the Utrecht summer school in geometry. The notes of the course can be found here. The intended audience are bachelor students with little or no background on manifolds.

2017/2018

I was the organiser of two reading seminars in Utrecht University (within the framework of the Friday Fish seminar):

  • Seminar on the microlocal theory of sheaves (where the leading organiser is Davide Alboresi)
  • Seminar on h-principle. Sadly, the seminar does not have its own webpage. We followed the usual references (the Eliashberg-Mishachev book and their papers in wrinkles), with the occasional help of my notes.

Docencia UAM 2015-2016

Durante dicho curso fui uno de los profesores de prácticas de Álgebra II de Físicas. A lo largo del cuatrimestre, David Alfaya y yo elaboramos unas hojas de soluciones para algunos de los ejercicios propuestos en las notas de Lucía Contreras.