# Java Darleen Villano

I am a fifth year Ph.D. candidate at the **University of Connecticut** (UCONN), working in mathematical logic.My Ph.D. 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 and gave a contributed talk at the 2024 North American Annual Meeting for the ASL. I was also at the CBMS Conference on Algorithmic Fractal Dimensions the week after.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.

## Publications and preprints

**Publications**

**The Ginsburg-Sands theorem and computability theory***Benham, H. et al**Advances in Mathematics*, vol. 444, 109618, 2024.

(arXiv preprint)

**Preprints**

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

**Summer 2024**

**(Upcoming) 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.**(Canceled) The New England Recursion and Definability Seminar**//**Dartmouth College**//**Title:**Computable categoricity relative to a c.e. degree**17th International Conference on Computability, Complexity, and Randomness**//**Nagoya University**//**Title:**Computable categoricity relative to a c.e. degree**SIGMA Seminar Spring 2024**//**University of Connecticut**//**Title:**The Ginsburg–Sands theorem and computability theory

This was a group SIGMA talk given by Heidi Benham, Andrew DeLapo, and me based on joint work with our advisors, Damir Dzhafarov and Reed Solomon.**SIGMA Seminar Spring 2024**//**University of Connecticut**//**Title:**Normality and Randomness

This was a talk that I gave on joint work with Wesley Calvert, Emma Gruner, Elvira Mayordomo, and Daniel Turetsky.**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**

**SIGMA Seminar Fall 2023**//**University of Connecticut**//**Title:**Randomness and Hausdorff dimension**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**SIGMA Seminar Fall 2022**//**University of Connecticut**//**Title:**When does the existence of an isomorphism imply the existence of a computable isomorphism?

**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.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.

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

## Teaching

For **Spring 2024**, I am an instructor for **Math 1071Q** (Calculus for Business and Economics). My office hours are **Wednesdays** at **1-2:30PM**.Below is a list of my previous teaching posts at the UConn Storrs campus since Fall 2019.

**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 am the current 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.