Math Interests

My math area is functional analysis in the branch of operator algebras. I'm interested in the side of C*-algebras, K-theory, and C*-dynamics. I also find very attractive the bunch of interactions between operator algebras and other branches of mathematics such as operator theory, graph theory, representation theory, ergodic theory, probability, and topology. 

Althought my main research direction are operator algebras, I find fascinating many types of mathematics. In particular, I identify myself as an analyst, and I'm a big fan of real-harmonic-&-functional analysis, measure theory, and probability.

My master's thesis is a monographic project about classification of irrational rotation algebras. This is a family of non-commutative C*-algebras that generalizes the algebra of continuous functions on the 2-dimensional torus.  

Participation in research projects

• Master's Thesis Seminar. (Summer 2023–Spring 2024) 

Subject: Classification of Irrational Rotation Algebras

Keywords: Universal C*-algebras of generated by relations, K-theory, AF-algebra associated to a continuous fraction, GNS-representation, Berg's Approximation Technique.

• Outsourcing Math Research "Looking for a Projection". Summer 2022. 

Subject: Introduction to Hilbert C*-modules and Pimsner-Popa basis

Keywords: C*-algebras, Hilbert C*-module, Pimsner-Popa basis, AF-algebras, K-theory, Bratteli diagrams. 

Outsourcing Math Research website.

• Undergraduate Research Seminar II. (Spring 2022)

Subject: Theory of Distributions.

Keywords: test functions, distributions, topology of the space of test functions, Dirac delta functions.

• Undergraduate Research Seminar I. (Fall 2021)

Subject: Measure Theory on the Sierpinski Gasket

Keywords: graph approximations, self-similar measures, energy of a graph, geometric and analytic properties of Sierpinski Gasket.

• CIMAT Summer Research Program. (Summer 2021)

Subject: The Moment Problem

Keywords: Historical notes about the moment problem, Jacobi matrices, quadratic forms, orthonormal polynomial sequences, equations on differences.

• Summer of Research of the Mexican Academy of Sciences. (Summer 2020) 

Subject: The Bargmann Space

Keywords: spaces of functions, Hilbert spaces, reproducing kernels, canonical commutation relations, Bargmann transformation, Stone-von Neumann theorem. You can consult a technical report that I wrote for this project.

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"I went to the woods because I wished to live deliberately, to front only the essential facts of life, and see if I could not learn what it had to teach, and not, when I came to die, discover that I had not lived."

-Henry David Thoreau

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