Alonso Delfín Ares de Parga was born and raised in Mexico City. He initially started an undergraduate degree in Economics at ITAM (Instituto Tecnológico Autónomo de México), but eventually switched to a degree in Applied Mathematics, also at ITAM. After completing his undergraduate degree, Alonso decided to pursue a career in pure mathematics and earned a Master of Science in Pure Mathematics from CINVESTAV-IPN (Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional). While completing his master's degree, he started teaching undergraduate Calculus courses at ITAM.

Right after his Master's graduation, Alonso moved to Eugene, OR, to pursue a PhD in Mathematics at the University of Oregon (UO) under the supervision of N. Christopher Phillips. While at UO, he conducted research in Functional Analysis, ran two Directed Reading Projects with undergraduate students, taught 14 undergraduate courses, and was a TA for several graduate courses in Analysis and Probability.

Alonso is currently a Burnett Meyer Postdoctoral Fellow at the University of Colorado Boulder, working with mentors Carla Farsi and Judith Packer. At CU Boulder, he engages in research and teaches both undergraduate and graduate courses. He has also spent two summers running REU(G) projects based on some of his research projects that are accessible to strong undergraduate students and early graduate students.

Alonso is married to Antonella, also from Mexico City, they've been together since high school and they have a son who was born while both were finishing their PhDs at the UO.

Since moving to the U.S., people often think Alonso's middle name is Delfín. Thus, he always likes to tell people that he does not have a middle name. His name follows conventional naming traditions from Mexico, which are also observed in most of Latin America and in Spain as well, that is, it consists of his given name: Alonso, his paternal last name: Delfín, and his maternal last name: Ares de Parga.

Alonso's research is in Operator Algebras, a subarea of Functional Analysis that requires tools from Algebra, Analysis, and (Algebraic) Topology. Informally, the study of Operator Algebras can be described as `infinite-dimensional linear algebra'. More concretely, an operator algebraist studies spaces of linear operators (i.e., matrices in finite dimensions) acting on potentially infinite-dimensional Banach spaces. The algebraic tools he works with are mostly the same as those in finite dimensions: for instance his research papers are likely to contain words such as kernels, images, simplicity, representations, modules, and Morita equivalence. The analytic aspect arises from the norms that allow topologies to be placed on these operator spaces. The algebraic topological component comes from the classification of such spaces, where tools such as K-theory and homology theories are widely used. Alonso’s research particularly focuses on operators acting on L^p-spaces, incorporating measure theory as a fundamental tool for him. Much of his work involves investigating results and properties of operators on Hilbert spaces (i.e., L^2-spaces) to determine whether they extend to operators on L^p-spaces for other values of p. In some cases, results do extend, but their proofs require significantly different techniques due to the absence of adjoint operators and orthogonality when p is not equal to 2.

Alonso has more than 10 years of teaching experience and has been passionate about teaching since his undergraduate years. He began tutoring and running help sessions early in his academic career. Immediately after earning his undergraduate degree, he was hired to teach Calculus courses at his alma mater. One of the reasons he chose the University of Oregon (UO) for his PhD was its policy allowing graduate students to be sole instructors of undergraduate courses from their first year. As a result, he has taught a wide variety of undergraduate courses (some in Spanish, most in English), including College Algebra, Trigonometric Functions, Differential Calculus, Integral Calculus, Vector Calculus, Differential Equations, Discrete Mathematics, Linear Algebra, Analysis, and Introduction to Proofs. His favorite course to teach is Discrete Mathematics—likely because it is far from his research area, and he finds the topics both interesting and challenging, making him particularly enthusiastic about explaining them to students. Additionally, he has TA’d for several graduate courses in Analysis and Probability, given numerous expository research talks, and taught a Topics in Functional Analysis course for graduate students at CU Boulder.

Mentorship has been a central part of Alonso’s academic career. At UO, he served as a mentor for incoming international graduate students, guiding a total of five students from different parts of the world during their first year in the program (Colombia, Iran, and Sweden). He also led two Directed Reading Programs for undergraduates and organized the PhD Boot Camp for incoming graduate students. At CU Boulder, he has mentored undergraduate and graduate students for two consecutive summers through REU(G) projects.

In terms of service, Alonso was a founding member of the AMS Graduate Chapter at UO and was elected its President for the 2021–2022 academic year after serving as Diversity Chair in 2020–2021. While at UO, he also organized the student Functional Analysis seminar. Now at CU Boulder, he co-organizes the department’s Functional Analysis seminar and has co-organized the Operator Algebras parallel sessions at the MAA Rocky Mountain Section for two years in a row. Since 2024, Alonso has also been an active reviewer for Mathematical Reviews and has refereed papers for journals specializing in Operator Algebras.

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“As a Latin American living in the U.S., Hispanic Heritage Month holds great significance for me. It is a time to raise awareness of how ubiquitous our presence is in this country. As a mathematician, I have encountered countless inspiring individuals who identify as Latine or Hispanic and are doing amazing work in science. This month is an opportunity to celebrate these diverse stories while also acknowledging the struggles behind them. By doing so, I hope we can continue to inspire future generations and show them that science—and particularly mathematics—can be pursued by anyone, anywhere.”

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