I am currently working on projects involving reverse mathematics and effective topology. One way to code topological spaces in computability theory is by restricting to countable second-countable (CSC) spaces; this was first studied by François Dorais in this 2011 paper. Fellow graduate students Heidi Benham, Java Darleen Villano, and I, along with our advisors Damir Dzhafarov and Reed Solomon, used the formalization of CSC spaces to provide a reverse-mathematical analysis of several aspects of the Ginsburg-Sands theorem in point-set topology. The result is our paper published in Advances in Mathematics here and on arXiv here.
My current work expands on some of the work from the Ginsburg-Sands project and involves techniques from classical computability theory, reverse mathematics, and the Weihrauch degrees.
I graduated from UC Berkeley in May 2020. I wrote my senior honors thesis, Bernoulli Randomness and Bernoulli Normality, under the supervision of Professor Theodore Slaman. The paper was published in Mathematical Logic Quarterly here. An earlier version is available as a pre-print on arXiv here.
Those who are interested in dynamical systems are encouraged to see the GitHub repository for the IFS Code Visualizer program I wrote as part of my senior honors thesis. My thesis ends on a few open questions regarding iterated function systems and randomness, and the IFS Code Visualizer allows for computational exploration of those questions. A web version is now available here.
Below, some JavaScript code is generating the Barnsley Fern using four different sequences. This code runs in the browser using the p5.js library for JavaScript. The code can be viewed here. The visualization demonstrates that the speed at which the Barnsley Fern is generated can vary for different sequences, even though the sequences are all Bernoulli normal to the same probabilities. It is unknown (to me, at least) whether the same fractals are generated if the sequences are all Bernoulli normal to the same probabilities. The biasing algorithm from my paper is also implemented in the code to bias Champernowne's, Copeland-Erdos's, and Besicovitch's sequences.
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