Java Darleen Villano

I'm Java, and I work in mathematical logic. I just earned my PhD in mathematics at the University of Connecticut (UCONN).My PhD advisors are Reed Solomon and Damir Dzhafarov.My email is javavill (at) uconn (dot) edu.Note: My entire first name is Java Darleen, but please feel free to just call me Java.

About me

I was born in the Philippines and moved to California when I was young. I grew up in California, and did most of my school there. I graduated from the University of California, Berkeley with a B.A. in Mathematics and a Logic minor in Spring 2019. I started at the University of Connecticut in Storrs as a mathematics Ph.D. student in Fall 2019.I recently attended the South Eastern Logic Symposium (SEALS) at University of Florida and gave a talk there on some of my current work.Outside of math, some of my hobbies include makeup, fashion, collecting cute items (stationary, plushies, etc.), and playing games.

Research interests

Most of my interests lie in computability theory. More specifically, I am interested in computable structure theory, algorithmic randomness, and reverse mathematics.Recently, I have been investigating the following relativization of computable categoricity: we say that a computable structure A is computably categorical relative to a degree d if for any d-computable copy B of A, there exists a d-computable isomorphism between A and B. I showed that being computably categorical relative to a c.e. degree is not a well-behaved notion here.

CV

My CV is available here.---If you were wondering, I use the RenderCV sb2nov Theme template, which can be imported easily into an Overleaf project.

Publications and preprints

Publications

  1. The Ginsburg-Sands theorem and computability theory Benham, H. et al
    Advances in Mathematics, vol. 444, 109618, 2024.
    (arXiv preprint)

Preprints

  1. Computable categoricity relative to a c.e. degree Villano, J.D. (arXiv preprint; submitted)

  2. Normality, Relativization, and Randomness Calvert, W. et al (arXiv preprint; submitted)

Talks

If you are looking for any of my slides from previous talks, please go to this link.

Spring 2025

  • South Eastern Logic Symposium (SEALS) // University of Florida // Title: Computable categoricity relative to a degree

  • Graduate Research Forum // University of Connecticut // Title: Relativizing computable categoricity

Fall 2024

  • The New England Recursion and Definability Seminar // Dartmouth College // Title: Computable categoricity relative to a c.e. degree

Summer 2024

  • Computable Structure Theory and Interactions // Technische Universität Wien // Title: Computable categoricity relative to a degree

Spring 2024

  • 2024 ASL North American Annual Meeting // Iowa State University // Title: Computable categoricity relative to a c.e. degree

  • AMS New England Graduate Student Conference // Brown University
    I gave two talks at this conference. I gave a lightning talk based on this paper, and a full talk based on some of my work in computable structure theory.

  • 17th International Conference on Computability, Complexity, and Randomness // Nagoya University // Title: Computable categoricity relative to a c.e. degree

  • Joint Mathematics Meeting 2024 // San Francisco, CA // Title: Computable categoricity relative to a c.e. degree
    This was an invited talk that I gave during the AMS Special Session on Computable Mathematics dedicated to Martin D. Davis.

Fall 2023

  • CT Logic Seminar // University of Connecticut // Title: Computable categoricity relative to a c.e. degree

Fall 2022

  • Ph.D. General/Oral Exam // University of Connecticut // Title: Computable Categoricity Relative to a Degree

  • Mathematics Continued Conference 2022 // University of Connecticut // Title: The undecidable and the undefinable

Spring 2022

  • AMS New England Graduate Student Conference // Brown University // Title: Priority arguments

Slides

This is where I will put links to my slides from talks I've given at conferences or in seminars. Please note there may be some minor errors in some of them.

  • Here are my slides for my Ph.D. Oral/General Exam, taken in Fall 2022. If you are currently a UCONN graduate student, please be aware that I took this exam before they clearly established the official guidelines for oral/general exams, so the content of these slides are more than is expected.

  • Here are my slides for a talk based on the point-to-set principle which I gave in a SIGMA Seminar in Fall 2023.

  • Here are my slides for a contributed talk on computable categoricity relative to a c.e. degree which I gave at the 2024 North American Annual ASL Meeting. Here is a version which has more details on the construction that I gave as part of an invited talk at CSTI 2024.

  • Here are my slides from dissertation defense from Spring 2025. They largely contain the same content covered in previous talks I've given on my work on categoricity relative to a degree.

---If you were wondering, I use the Metropolis Beamer Theme for my beamer talks. This theme can be used in Overleaf.

Teaching

For Spring 2025, I am a TA for Math 2110Q (Multivariable Calculus). My office hours are Tuesdays from 11AM-12PM and Wednesdays from 2:30-3:30PM.Below is a list of my previous teaching posts at the UConn Storrs campus since Fall 2019.

  • Fall 2024 — Instructor, Math 1071Q (Calculus for Business and Economics)

  • Spring 2024 — Instructor, Math 1071Q (Calculus for Business and Economics)

  • Fall 2023 — Instructor, Math 1071Q (Calculus for Business and Economics)

  • Spring 2023 — Instructor, Math 1071Q (Calculus for Business and Economics)

  • Fall 2022 — Teaching Assistant, Math 1132Q (Calculus II)

  • Spring 2022 — Teaching Assistant, Math 1132Q (Calculus II)

  • Fall 2021 — Teaching Assistant, Math 1131Q (Calculus I)

  • Spring 2021 — Teaching Assistant, Math 1132Q (Calculus II)

  • Fall 2020 — Teaching Assistant, Math 1132Q (Calculus II)

  • Summer 2020 — Course Tutor with Student Support Services, Math 1070Q (Mathematics for Business and Economics)

  • Spring 2020 — Teaching Assistant, Math 1132Q (Calculus II)

  • Fall 2019 — Teaching Assistant, Math 1131Q (Calculus I)

Outreach

I was a President of the UConn Chapter for the Association for Women in Mathematics.I was a speaker at the Mathematics Continued Conference in Fall 2022. The MCC seeks to give undergraduate students interested in math an opportunity to learn about graduate school and current research done by graduate students and faculty.