This section gathers courses with their own page, video playlists where available, and a year-by-year chronology.

I teach in the mathematics graduate programme at CIMAT, in the graduate programmes at UNAM and UADY, and at the undergraduate level (UADY, and previously UNAM-FC, ITAM, ITESM, Concordia).

Thesis supervision, postdocs, summer stays and research fellows have a dedicated page: Students and training (summary, tables and contact email for prospective students).

Video material is available on the YouTube channel.

2026

• Condensed Mathematics II – Sites, sheaves and condensation (MC-II-2026-2, Clausen–Scholze / Le Stum series).

2025

• Condensed Mathematics I – Categorical and topological foundations (UNAM Graduate Programme, August 2025, online).
• Number Theory and Discrete Dynamical Systems: Deciphering the Dynamics of Genetic Networks – mini-course given at the CIMAT-Merida Summer School 2025 (30 Jun – 4 Jul 2025).

2024

• Selected Topics in Algebraic Geometry III – Elliptic curves and schemes (90SGAL03, online).

2023

• Non-Archimedean dynamics (Berkovich spaces) (18SGAL01, CIMAT).
• TSGA – Schemes and arithmetic curves (CIMAT, Aug–Jan 2024).
• Elliptic curves (UNAM, UADY).
• p-adic dynamical systems and applications (CDPA2023, UNAM Master’s).

2022

• TSGA II – Galois groups and fundamental groups (CIMAT).
• Galois Theory (UADY).
• Algebraic number theory (CIMAT, FMat U de G) – Videos TAN.

2021

• Selected Topics in Algebraic Geometry I and II (Schemes and arithmetic curves), CIMAT Doctoral Programme: Videos GAE1, Videos GAE2.
• p-adic Galois Representations – mini-course given by invitation at the CIMPA Research School: Hodge Theory and p-adic Hodge Theory (CIMAT-Guanajuato, 2–10 Aug 2021, virtual school). Videos on YouTube.

2020

• Mathematics for Engineering I (UTP Yucatan).
• p-adic Galois representations (90SGAL01, UNAM) – Videos RGP.
• Galois groups and the fundamental group (CIMAT-Merida Summer School) – Videos.
• Introduction to p-adic analysis (UADY).

2019

• Introduction to cryptography and number theory (UADY).
• Arithmetic algebraic geometry (UADY).

2018

• Commutative algebra (UADY).
• p-adic geometry (Berkovich spaces) (CIMAT Doctoral Programme).

2017

• Cryptography I (UADY).
• Algebraic number theory (UADY) – uady-tan.wikidot.com.

Earlier years (2001–2014)

Concordia University, Montreal, Canada

• 2008: Math 206 Algebra & Functions (fall, 43 students); Math 203 Differential & Integral Calculus I (winter, 49 students)
• 2009: Math 203 Differential & Integral Calculus I (fall, 65 students)
• 2010: Math 208 Fundamental Mathematics I (fall, 58 students)
• 2011: Math 206 Algebra & Functions (summer, 44 students)
• 2011–2013: Math Help Centre – Tutor Leader grade 1 (Calculus I and II, Vectors and Matrices).

Universidad Anahuac del Norte, Mexico City

• 2005: Differential and Integral Calculus I; Linear Algebra; Advanced Mathematics for Engineering.

ITAM, Mexico City

• 2005: Mathematical Methods for Finance (Master’s in Economics).
• 2006: Linear Algebra; Algebra for Engineers II.
• 2014: Mathematics I; Calculus III; Quantitative Methods for Finance.

ITESM, Mexico City

• 2014: Mathematics I.

UNAM – Faculty of Sciences, Mexico City

• 2001: Mathematics I (for Biologists).
• 2006: Complex Variable I; Linear Algebra I; Number Theory I.
• 2014: Number Theory I.

Teaching assistance

• 1998–2004 (UNAM-FC): Teaching Assistant – Higher Algebra I (1998), Higher Algebra II (1999), Algebra Seminar A (1999), Algebraic Geometry II (2000), Mathematics I (2000), Algebra Seminar B (2001).
• 1998–1999 (UNAM/SMM): Coach, Mathematical Olympiads.
• 2011–2013 (Concordia): Math Help Centre – Tutor Leader.

Videos: YouTube Channel.

Students, postdocs and fellows: Students and training. More links: Courses with a page | Events and talks | Outreach | Projects.