curriculum vitae

• I began my master's degree in science at CIMAT in August 2022, engaging in specialized courses tailored to my research interests and participating in schools focusing on intriguing topics.

• Between August 2018 and June 2022, I pursued a Bachelor of Science in Mathematics at the University of Guanajuato, exploring various mathematical domains, including probability, Fourier analysis, and operator algebra. 

From February 2021 to May 2023, I served as a Teaching Assistant at the University of Guanajuato, aiding in Vector Calculus and Real Analysis I for undergraduate students, and as a Teaching Assistant in Algebra, Calculus, and Geometry for High School students at CIMAT during the Spring of 2023, Fall of 2022, and Spring of 2021. 

• My involvement in the Mathematics Olympiads extended from 2011 to 2018, shaping my skills in constructing logical arguments and nurturing abstract thinking.

mathematical interests

Mathematical Interests: My primary focus is functional analysis, particularly operator algebras. My master's thesis explores operator K-theory, C*-algebras, AF-algebras, and the classification of C*-algebras.

Thesis Work: I'm crafting my master's thesis with Dr. Roberto Hernández Palomares (University of Waterloo) as my advisor and Dr. Stephen Sontz (CIMAT) as my co-advisor. It revolves around Elliott's classification theorem, which deals with classifying AF-algebras by their ordered K_0-groups.

Favorite Graduate Courses: In graduate school, I enjoyed C*-algebras, von Neumann algebras, Free Probability, and Functional Analysis. As an undergraduate, I was captivated by Measure Theory, Harmonic Analysis, Real Analysis, Abstract Algebra, Galois Theory, Algebraic Geometry, and General Topology.

Research projects (past and present)

• Total Positivity, January 2023. Part of the 8th Oaxaca Winter School of Mathematics at UNAM. Under the guidance of Dr. Lara Bossinger and Dr. Alfredo Nájera Chávez, I delivered a presentation based on the article "Total positivity: tests and parameterizations" (2000) by Fomin and Zelevinsky.

Here are the slides of the presentation (in Spanish)

Topics: Double Wiring Diagrams and Total Positivity Criteria.

• Looking for a Projection, June 2022 - August 2022. Under Dr. Roberto Hernández Palomares (University of Waterloo) and in collaboration with José Manuel Barrientos López (CIMAT). Focused on C*-algebras theory with readings from "C*-algebras by example" and "An Introduction to K-Theory for C*-Algebras." 

Topics: Introduction to C*-algebras, Hilbertian modules and K-theory.

• Introduction to Monothectic Groups, January 2022 - May 2022. Under Dr. Manuel Cruz López (University of Guanajuato). 

Topics: Topological groups, monotectic groups, Haar measure, monotectic group structure theorems and character groups.

• Introduction to p-adic Analysis, January 2019 - November 2021. Led by Dr. Manuel Cruz López (University of Guanajuato). In collaboration with Dennis Diaz Diaz (CIMAT), Jesus Martinez Miranda (CIMAT), Sergio Nishimura Vallarta (University of Guanajuato), and Nuria Sydykova Mendez (University of Guanajuato). 

Here, I'm sharing some of the problems we collectively solved as a group. Additionally, I'm providing slides of a presentation I delivered on p-adic numbers (in Spanish).

Specific topics: p-adic analysis.

• Numerical Probability of Ruin Estimation, June 2020 - July 2020. At the University of Guanajuato Summer of Scientific Research program under Dr. Ehyter M. Martín González. 

Specific topics: Extreme value distributions, Cramer-Lundberg model, probability of ruin, return periods and fit coefficient estimation.

Talks

You can find one of my talks about my thesis project here.

Training activities 

• Thematic Program on Operator Algebras and Applications. Fields Institute, Toronto, Canada November 2023. I attended the Twinned Conference on C*-Algebras and Tensor Categories and Workshop on Operator Algebras and Applications: Free Probability.

• Groundwork for Operator Algebras Lecture Series, Purdue University, West Lafayette, IN, USA, June 2023. Two-week intensive course on operator algebras, including lectures on C*-algebras and von Neumann algebras, problem-solving sessions, and expository and workshop talks.

• Summer School: Geometría Prohibida (Forbidden Geometry), Universidad Autónoma de San Luis Potosí, Mexico, July 2022. A week-long thematic school featuring talks and workshops on concealed geometry across various mathematical disciplines.

• Algebraic Geometry School. Universidad Autónoma de Zacatecas, August 2021.

• CIMAT Summer School, July 2021.

• CIMAT Merida Virtual Summer School, July 2020. I took five mini-courses, notably "Thinking in Parallel," a workshop on parallel programming, and "Galois Groups and Fundamental Groups: A Perspective from Algebraic Geometry and Arithmetic."

• 10th Virtual Summer School UNAM: Machine learning in systems biology, June 2020.

• XVI Taller de Solución de Problemas de Cálculo (16th Calculus Problem Solving Workshop), CIMAT, Guanajuato, Mexico, July 2019. I participated in a guided project on random walks and additional topics including cryptography and coding theory.

further experience

• Cuarto Encuentro Nacional de Estudiantes de Posgrados en Matemáticas (IV National Meeting of Mexican Graduate Students in Mathematics), Cuernavaca, Mexico, June 2023. Academic event with 63 graduate students in mathematics from various institutions all across Mexico.

• Coloquio de mujeres en ciencia para mujeres (Colloquium on Women in Science for Women), CIMAT, Guanajuato, Mexico, May 2023. A three-day colloquium showcasing talks by women researchers in STEM and round tables on different themes.

Training activities 

• Thematic Program on Operator Algebras and Applications. Fields Institute, Toronto, Canada November 2023. I attended the Twinned Conference on C*-Algebras and Tensor Categories and Workshop on Operator Algebras and Applications: Free Probability.

• Groundwork for Operator Algebras Lecture Series, Purdue University, West Lafayette, IN, USA, June 2023. Two-week intensive course on operator algebras, including lectures on C*-algebras and von Neumann algebras, problem-solving sessions, and expository and workshop talks.

• Summer School: Geometría Prohibida (Forbidden Geometry), Universidad Autónoma de San Luis Potosí, Mexico, July 2022. A week-long thematic school featuring talks and workshops on concealed geometry across various mathematical disciplines.

• Algebraic Geometry School. Universidad Autónoma de Zacatecas, August 2021.

• CIMAT Summer School, July 2021.

• CIMAT Merida Virtual Summer School, July 2020. I took five mini-courses, notably "Thinking in Parallel," a workshop on parallel programming, and "Galois Groups and Fundamental Groups: A Perspective from Algebraic Geometry and Arithmetic."

• 10th Virtual Summer School UNAM: Machine learning in systems biology, June 2020.

• XVI Taller de Solución de Problemas de Cálculo (16th Calculus Problem Solving Workshop), CIMAT, Guanajuato, Mexico, July 2019. I participated in a guided project on random walks and additional topics including cryptography and coding theory.

further experience

• Cuarto Encuentro Nacional de Estudiantes de Posgrados en Matemáticas (IV National Meeting of Mexican Graduate Students in Mathematics), Cuernavaca, Mexico, June 2023. Academic event with 63 graduate students in mathematics from various institutions all across Mexico.

• Coloquio de mujeres en ciencia para mujeres (Colloquium on Women in Science for Women), CIMAT, Guanajuato, Mexico, May 2023. A three-day colloquium showcasing talks by women researchers in STEM and round tables on different themes.

current and past ACADEMIC AND SOCIAL SERVICE