Appointments :

2019-present. Associate Professor. Universidad del Valle.

10/2018- 2019. Research Associate, Leverhulme Trust Project. Queen Mary University of London.

07/2014-10/2018 Research Associate, Leverhulme Trust Project. Imperial College London.

06/2012-06/2014 Research Associate, Marie Curie Incoming International Fellow. Imperial College London.

Education :

2005 (PhD) Docteur de l'Université Pierre et Marie Curie (Now Sorbonne Université). Bornitude Lp pour une classe d'opérateurs pseudo-différentiels dans le cadre du calcul de Weyl-Hörmander. Mention très honorable. Harmonic Analysis. Jury : Michael E. Taylor(U. North Carolina at Chapel Hill), Chao Jiang Xu(U. Rouen), Jacques Faraut(U. Paris 6), Sami Mustapha(Advisor)(U. Paris 6).

2002 D.E.A d'Analyse (Master's degree). Université Pierre et Marie Curie. Sur la bornitude L2 de l'integrale de Cauchy. Real Analysis and Potential theory.

2000 M.S, Mathematics. Universidad del Valle. Caracterización de los operadores nucleares en Lp. Functional Analysis.

1997 B.S. Mathematics. Summa Cum Laude. Universidad del Valle. Normas de los operadores de rango finito en un espacio de Hilbert. Functional Analysis.

Referee :

I am referee for the mathematical journals : Applied and Computational Harmonic Analysis, Journal of Fourier Analysis and Applications, Comptes Rendus Mathematique, Bulletin des sciences mathématiques, Proc. Amer. Math. Soc., Integral Equations and Operator Theory, Analysis & PDE, Bull. London Math. Soc, Journal of London Mathematical Society, Math. Nachr, Banach Journal of Mathematical Analysis, Reports on Mathematical Physics, Journal of Pseudo-differential operators and Applications, Math. Model. Nat. Phenom, Indian Journal of Pure and Applied Mathematics, Iranian Journal of Mathematics, Revista Colombiana de Matematicas, Revista Integracion, Revista Enseñanza Universitaria, among others.

I have been Book referee for CRC Press and Springer.

PhD Students

2019-Cosupervising: Duvan Cardona. Ghent University, Belgium

2015-2019 : Andres Muñoz. On the differentiability of Lipschitz functions on Banach spaces. Universidad del Valle.

Co-supervisor of several PhD students. Imperial College London.

Examiner for PhD first year and second year projects. Imperial College London

Master Students

Frederick Opoku. On a Class of Vector-Valued Pseudo-Differential Operators and Partial Differential Equations. University of Ghana. 2021

Carlos A. Rodriguez. Lp bounds for pseudodifferential operators on Zn, Universidad del Valle, 2011.

Undergraduate Students

Sebastian Vargas. On the Approximation property on Banach spaces. Universidad del Valle. 2021

Duvan Cardona. Invertibility of non-elliptic operators, Universidad del Valle, 2013.

Oscar E. Escobar. El problema de Dirichlet. Universidad del Valle. 2009.

Alex Zamudio. Invertibilidad para una clase de operadores elipticos degenerados en el marco del calculo de Weyl-Hörmander . Universidad del Valle. 2008

Wilmar Bolaños. El problema de la traza en Lp. Universidad del Valle. 2007.


2012-2014 Marie Curie Incoming International Fellowship. European Comission.

2002-2005 Award by Mazda Company. Grant to pursue graduate studies given to the best top 10 students of Music and Science of Colombia.

1997-2000 Universidad del Valle Scholarship.

Research Projects

2020-2021 Well-posedness for a class of pseudodifferential parabolic equations on the torus. Grant Univalle

2019-2020 Pseudodifferential calculus and Spectral Theory. Grant Univalle

2017-2020 Analysis in the phase-space. Leverhulme Trust. Imperial College London and Queen Mary University.

2014-2017 Quantization on Nilpotent groups and Analysis on the phase-space. Leverhulme Trust. Imperial

College London.

2012-2014 Pseudo-Differential Operators and Operator Ideals. Grant under Marie Curie International Incoming

Fellowship. Imperial College London.

2011-2012 Lp estimates for pseudodifferential operators on the torus. Grant Univalle.

Principal investigator : Julio Delgado.

2009-2010 - Invertibility for degenerate elliptic operators. Grant. Univalle.

Principal investigator : Julio Delgado.

2008-2009 - The trace of nuclear operators on Lp spaces. Grant Viceinv. Univalle

Conference organizer

2012-2018 co-organiser of the Pure Analysis and PDEs seminar at Imperial College London.

Analysis and PDEs (Funded by EPSRC GCRF for developing countries). http ://wwwf.imperial.ac.uk/ ruzh/ICconference-oda.htm Imperial College London, UK, 26-30 September, 2016.

Noncommutative Analysis and PDEs. http ://wwwf.imperial.ac.uk/ ruzh/IC-conference-noncommutative.htm

Imperial College London, UK, 11-15 April, 2016.

Microlocal Day # 5. Imperial College London, UK, 16 January, 2015.

CIMPA-UNESCO-REALMA-COLOMBIA School, Mathematics for Modeling and Simulation. Cali, Colombia,

11-22 June , 2007

Languages : English(fluent), French(fluent), Spanish(native).