# Java Darleen Villano

I am a fourth year Ph.D. candidate at the **University of Connecticut** (UCONN), working in mathemetical logic.My Ph.D. advisors are David 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 about 7 years old. 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 **UCONN** as a mathematics Ph.D. student in **Fall 2019**. For most of my mathematical career, I have been primarily interested in mathematical logic such as model theory and computability theory. Nowadays, I am mostly doing work in the latter.In **Summer 2022**, I attended the IMS Graduate Summer School in Logic, where I learned a lot of logic and also had the chance to explore the beautiful country of Singapore. Very recently, I was at a BIRS 5-day Workshop in computable structure theory, analysis, and randomness, where I had the chance to work with wonderful people while being surrounded by sights of the Rocky Mountains.Outside of math, some of my hobbies include makeup, fashion, collecting cute items (stationary, plushies, etc.), and playing games. Games that I play consistently include Final Fantasy XIV and Arknights.

## Research interests

Most of my interests lie in computability theory, computable structure theory, and algorithmic randomness.Recently, I have been investigating the structure of the c.e. degrees in relation to 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*.Some questions we could ask is for degrees **d** such that there exists a structure which is computably categorical relative to it (or not computably categorical relative to it), where can we find them below **0'**? Where are they between **0'** and **0''**?

## Publications and preprints

*Computable categoricity relative to a degree*(in preparation)

## Talks

**Fall 2022**

**Ph.D. General/Oral Exam**//**UCONN**//**Title:**Computable Categoricity Relative to a Degree

The Ph.D. General/Oral Exam is the "oral part" of the qualification exams for Ph.D. candidacy at UConn. I took my oral exam in Fall 2022. For my presentation, I covered an overview of the investigations into computability categoricity, relative computable categoricity, and how these two notions are related. I also presented some results from my research project in investigating the structure of the c.e. degrees where there is a computable structure that is (or is not) computably categorical relative to it. My slides are available here.**Mathematics Continued Conference 2022**//**UCONN**//**Title:**The undecidable and the undefinable**SIGMA Seminar Fall 2022**//**UCONN**//**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

Priority arguments have been a powerful tool since their introduction in providing an answer to Post’s problem in several areas in mathematical logic, such computability theory and model theory. We give a brief introduction to them and their different versions, and then cover some classical constructions. Afterwards, we will shift to their applications in computable structure theory in constructing certain examples in the study of the notion of relative computable categoricity.

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

## Teaching

For **Spring 2023**, I am an instructor for **Math 1071Q** (Calculus for Business and Economics). My office hours are **Mondays** at 1-3PM and **Thursdays** at 3-4PM. These hours may change during the first few weeks of spring semester.Below is a list of my previous teaching posts at the UCONN Storrs campus since Fall 2019.

**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.