Teaching and Seminars

Directed Bachelor Thesis

II-2023: I supervised three Bachelor monographs in Mathematics at Universidad del Norte.

  • Gabriel Ayala: Analysis of Graphs: Spectral Theorem and Communities Detection.
  • David Barco: Manifolds, Stokes Theorem and Differential Forms. 
  • Naim German Zuluaga Ramirez: Hyperbolic Space and Kleinian Groups: Constructing Hyperbolic 3-Manifolds.

Summer semester 2017: I supervised two Bachelor thesis in Mathematics at University of Luxembourg. 

  • Joel Costa: Spectral Theory on the hyperbolic plane. 
  • Loqman Salamatian: Gromov Compactness Theorem. 

Courses Taught

Universidad del Norte. Barranquilla, Colombia, 2019 – 2024

  1. II semester 2023: In-person. Calculus 1  and Differential Equations. (9 hours/week).
  2. I semester 2023: In-person. Calculus 1 and Differential Geometry. (9 hours/week). 
  3. I semester 2022: In-person. Differential Equations x3 and Differential Geometry. (12 hours/week).
  4. II semester 2021: Online. Differential Equations x2 and Calculus 1. (12 hours/week).
  5. I semester 2021: Online. Differential Equations x3 and Differential Geometry. (12 hours/week).
  6. II semester 2020: Online. Differential Equations x3 and Linear Algebra. (12 hours/week).
  7. I semester 2020: Started in-person, finished online. Differential Equations (big course) and Differential Geometry. (9 hours/week.)
  8. II semester 2019: In-person. Calculus 1 x2. (12 hours/week).
  9. I semester 2019: In-person. Analysis 2 and Calculus 1. (10 hours/week).


University of Luxembourg, Luxembourg, 2015 – 2018

  1. Summer semester 2018: Lecture on Functional Analysis. 
  2. Summer semester 2017: Lecture on Functional Analysis. 
  3. Winter semester 2016: Tutorial for Mathematical Structures.
  4. Summer semester 2015: Lecture on Functional Analysis. 


Universidad de los Andes, Bogota, Colombia

2009

  1. I semester 2009: Linear Algebra and Vector Calculus.
  2. II semester 2009: Linear Algebra and Complex variables.

2001 – 2003

  1. I semester 2002: Differential Calculus (reinforced).
  2. II semester 2002: Differential Calculus and Integral Calculus.
  3. I semester 2003: Integral Calculus and Linear Algebra.

Mathematical Institute, University of Bonn, Bonn, Germany, 2004 – 2005

I taught tutorial for the following lectures:

  1. Summer Term 2005. Analysis 2 for Prof. Dr. J. Franke.
  2. Winter Term 2004-2005. Analysis 3 for Prof. Dr. K. Th. Sturm.
  3. Summer Term 2004. Analysis 2 for Prof. Dr. K. Th. Sturm.

Co-organized Seminars

Topology and Geometry seminar at the University of Luxembourg. Feb 2017-Sept 2018. Co-organizer.

Working group on inverse spectral problems at the University of Nantes, winter semester 2014. Co-organizer.

Informal research seminar on Analysis at the Max Planck Institute for Gravitational Physics. June 2012 – March 2013. Co-organizer.

Research seminar on Geometry and Topology at the Universidad de los Andes. Second semester of 2009. Co-organizer.