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I am just trying to be a mathematician... looking for a place in the dark side of the universe.
I am just trying to be a mathematician... looking for a place in the dark side of the universe.
About me:
About me:
I had a postdoctoral fellowship until August of the current year at Instituto de Investigaciones Matemáticas Luis A. Santaló (IMAS) - UBA - CONICET. I was working under supervision of Dra. Andrea Solotar.
I received my Ph. D in November 2016 at National University of Colombia (Bogotá), under the orientation of Dr. José Oswaldo Lezama.
I obtained my master degree in Maths (Magister en Ciencias-Matemáticas) in July 2009 and my professional degree in Maths (Profesional en Matemáticas) in June 2007, both of them at the National University of Colombia (Bogotá).
My principal research areas are related with computational algebra and ring theory. Specifically, I have been working with non-commutative Gröbner bases for some algebras of polynomial type, besides developing several algorithms for computing projective dimension, bases for free modules, tools for determining whether a given module is stably free, and another similar results. In addition, I have studied the behavior of finitely generated projective modules over various class of rings, and topics related as non-commutative localizations, homological dimensions and diverse stabilization problems.
Currently, I am studying representations of skew PBW extensions, classification of Hopf algebras from a categorical point of view, Hopf actions over algebras similar to Weyl algebras and the stable rank of several associative algebras defined by polynomial relations.
Another research interests are related with algebraic topology, differential geometry, Lie algebras and several topics of Mathematical Physics.
Publications and Preprints
Publications and Preprints
Gallego, C. and Lezama, O., Gröbner bases for ideals of skew PBW extensions, Communications in Algebra, 39 (1), (2011), 50-75.
Gallego, C. and Lezama, O., Matrix approach to noncommutative stably free modules and Hermite rings, Algebra and Discrete Mathematics, 18 (1), (2014), 110-139.
Gallego, C. and Lezama, O., d-Hermite rings and skew PBW extensions, São Paulo Journal of Mathematical Sciences, 10 (1), (2016), 60 - 72.
Gallego, C., Matrix computations on projective modules using noncommutative Gröbner bases, Journal of Algebra, Number Theory: Advances and Applications, 15 (2), (2016), 101 - 139.
Gallego, C., Filtered-graded transfer of noncommutative Gröbner bases, Revista colombiana de Matemáticas, 50 (1), (2016), 41 - 54.
Gallego, C. and Lezama, O., Projective modules and Gröbner bases for skew PBW extensions, Dissertationes Mathematicae, 521, (2017).
Gallego, C., Solotar, A., Stable rank of down-up algebras, Journal of Algebra, Available online 22 March 2018. In Press, Accepted Manuscript.
Gallego, C., Algunas observaciones acerca del rango estable de anillos no conmutativos. Preprint.
Teaching experience
Teaching experience
National University of Colombia (Bogotá), Department of Mathematics. February 2008 - July 2013.
Subjects: Differential and integral calculus, Differential equations, Linear algebra, Groups and rings, Vectors and matrices, Basic math and Vectorial calculus.
University of Bogota Jorge Tadeo Lozano, Department of Basic Sciences. August 2011 - October 2016.
Subjects: Differential and integral calculus, Differential equations, Linear algebra, Basic math and Vectorial calculus.
University of Los Andes, Department of Mathematics. February 2016 - October 2016.
Subjects: Differential and integral calculus, Linear algebra.
Sergio Arboleda University, Department of Mathematics. August 2019 - Currently.
Subjects: Applied linear algebra, Optimization methods.
Pontifical Xaverian University, Department of Mathematics. June 2021 - Currently.
Subjects: Vectorial calculus, Linear algebra, Representation theory of groups.
Some related links
Some related links
Contact
Contact
E-mail: cmgallegoj@gmail.com
A copy of my CV can be obtained here.
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