Research
Research
In mathematics, I am interested in several different areas. Those of note include quantum entropy and inverse problems. I am motivated by the desire for unified mathematical models of abstract formal systems that admit application to diverse areas of mathematics in addition to physics, computer science, philosophy, and beyond.
"Deriving the Entropic Uncertainty Principle from Entropic Certainty Relations" (in progress)
I am currently working on a new derivation of the entropic uncertainty relation of Beckner–Białynicki-Birula–Mycielski from an entropic certainty relation. This project is inspired by work of Casini, Magan, and Martinéz in weakly coupled gauge theories.
"Conditions for the Simultaneous Recovery of Speeds and Sources of Waves on Graphs" with Amir Moradifam. (in progress)
"Inverse Wave Problems on Graphs" with Amir Moradifam. (submitted)
In this project we formulate and provide sufficient conditions for the solution of two inverse wave problems on finite graphs. Assuming known graph geometry, we study the recovery of the initial signal or the vertex wave speeds when the other is given. The source-recovery problem is equivalent to observability of the associated finite-dimensional system. The coefficient-recovery problem is solved under a zero forcing condition and a nonharmonicity assumption.
In philosophy, I think mostly in phenomenological and epistemological terms. I am deeply concerned with the problem of subjectivity and in particular of allowing an (optimistic) epistemological foundationalism for a univocal theory of mind. I have a strong interest in the history of philosophy—in particular the 19th century—with a focus on Fichte, Schelling, Hegel, and Kierkegaard. I am also interested in 20th century continental philosophy, most notably Bataille.
"On the mathematical infinite in Hegel's Science of Logic and the foundations of analysis" (in progress)
In this essay I carefully examine Bertrand Russel's claim that concepts like 'continuity' and 'the infinite' were placed on firm foundations by mathematicians in the late 19th and early 20th century and thereby disentangled from the "metaphysical nonsense" of philosophers like Hegel. I claim on the contrary that Hegel's critique of the differential calculus in the Science of Logic anticipates and preemptively responds to these developments, and that he is rather vindicated by the contributions of Cantor and Lebesgue.
"On the Faculty of Intuition" (2020). UVM Patrick Leahy Honors College Senior Theses. 377.
In this work I present an account of the faculty of intellectual intuition as analogous to the faculties of empirical sensing (i.e. sight, touch, hearing, proprioception, &c.). I develop an abstract schema into which all of these can be understood as 'presentational' mental activity. I then offer some external criteria that help distinguish between presentational mental activity which can justify belief (like intuition or seeing) and presentational mental activity that cannot justify belief (like dreaming or hallucinating). In the second chapter, I leverage the foregoing to defend epistemological foundationalism. Finally, I leverage my account of intuition specifically to defend against philosophical skepticism.