UIC PhD Dissertation, Published in 2022. Establishes minimal logical foundations for the definition and analysis of genetic functions whose image takes values over the Surreal number field, and introduces the notion of Veblen rank to bind the growth of complexity of said functions. 

Partially completed paper whose novel results appear in my dissertation; providing the motivation for the work that lead to Veblen rank.

Incomplete notes whose research program partially inspired my dissertation work; the topics extend from the summary of differentiation and attempts for integration of the surreals as well as exploring connections between Class sized models of set theory in which the Surreal numbers can be embedded and the automorphism between the surreal numbers in some ground model and the forcing extension.

A review document that I prepared for some of my perspicacious Calculus III students at UIC (this may be useful for other students studying Calculus III or interested in learning some of the fundamentals for Differential Geometry). 

A joint paper co-written by myself and two other graduate students for Lev Reyzin's Mathematics of Artificial Intelligence course - our principal result finds an example proving a conjecture of Alon et al that sign rank and dual sign rank do not agree. 

My dissertation for my MMath degree at the University of Waterloo; a broad historical survey of the subject of topos theory connecting the original motivations in algebraic geometry (the Weil conjectures), with recent developments in formal proof verification and functorial semantics.

Personal notes that informed a talk given in a course on Homotopy Type Theory at the University of Waterloo and Perimeter Institute in 2014.

Personal notes informing the content of two talks given at at the University of Waterloo's Graduate Seminar in Algebraic topology; a survey introducing the conceptual terms of category theory with the aim of motivating and defining derived functors.

A survey intended to provide an introductory overview for the formalisms found in introductory courses on quantum mechanics- chiefly the role played by Hilbert spaces.

A paper co-authored with 3 other students at Columbia's summer 2011 REU; we construct sequences of Apollonian group generators with infinite length to identify self-similar unbounded packings and connect such words with non-trivial residual points.