Audiences in Mathematics
My core research question as a philosopher has been "to what extent, and how, is mathematical proof affected by audience consideration?" I've worked on this project in various forms, as an undergraduate and graduate student. So far, it has resulted in two publications. The most recent publication is in Synthese (link here). It forms the core of my response to these questions. A video recording of a related talk, presented at the TPMP last summer, can be found here. The second publication is the result of a presentation at the 2017 CSHPM Meeting (link here). In it, I focus on the influence audience interest can have on project choice.
Mathematical Rigor
Recently, my research has pivoted toward the issue of informal rigor in mathematical proofs. What makes a proof informally rigorous and how does that connect, if at all, to formal rigor? I began thinking about these questions in my candidacy project. I specifically was interested in the extent to which the term rigor was an open-concept and what effects that had on the view that informal rigor is intimately tied to the ability to formalize a proof.
Moving forward, I want to tie the notion of informal rigor to the work I've done on audiences. I'm specifically interested in the social component of rigor. I begin some work toward this in my 2021 BSHM-CSHPM talk (conference info link here) where I argue for formal rigor as defining a certain mathematical argumentative environment. In my dissertation, I present and argue for a new account of mathematical rigor which grounds rigor judgments in terms of imagined, universal audiences.
Please reach out if you're interested in either of these drafts.
Statistics and Philosophy
One of my key interests lies at the intersection of statistics and philosophy. I use statistical methodology to inform philosophical questions. I also use philosophy to examine and reflect on statistical practice.
Focusing on the first direction, I have worked extensively with Moti Mizrahi on experimental philosophy projects. We take a data-driven approach to philosophical questions and have published two papers using this approach. The first (link here) focuses on determining whether or not linguistic markers which indicate appeals to intuition are in fact correlated with discussions about intuition in the philosophical literature. Our second paper (link here) tests a common assumption that philosophy is in the business of giving mainly deductive arguments.
On the second direction, I've been interested in questions of statistical explanations. One recent project focuses on Regression to the Mean as a scientific explanation. In the paper, which was presented at the 2019 Pacific APA, I use RTM to explore the boundaries of causal explanation and the explanatory force of non-causal explanation.
Statistics
Broadly my statistical research interests lied in how humans interacted with data and how data stood to affect them. I worked on two main projects in statistics during my undergraduate studies.
At LANL, I focused on visualization methods for big data. More specifically, I designed and analyzed studies for testing the efficacy of colormaps in feature identification. Information about the overall project can be found at this link where you can find colormaps quite similar to the header of this page. My technical report on the project can be found here.
My second major project was on identifying factors for predicting the progression of chronic kidney disease. I focused on clinical and genomic features: features that could easily be identified and used by doctors for preventive measures. You can read a news article about it here or download the abstract here. I gave two poster presentations on this research. In addition, we published a paper in Frontiers in Big Data, available here.