I am a mathematician working in quantitative trading. I received my Ph.D. in math from Stanford in August 2020, advised by Ravi Vakil and Jarod Alper.
My academic research interests are largely in algebraic geometry, with a focus on moduli theory and the formal geometry of algebraic stacks. See my papers below.
Before coming to Stanford, I was an undergraduate in math at the Australian National University, advised by Jarod Alper and David Ishii Smyth.
Papers
Formal Geometry of Algebraic Stacks
Coherently complete algebraic stacks in positive characteristic
This paper partially generalizes the main algebraization theorem of Alper-Hall-Rydh to the reductive case. We prove for a reductive group $G$ acting on an affine scheme of finite type $X/k$ with $A^G = k$ and $X^G \neq \emptyset$ that $[X/G]$ is coherently complete along the unique closed point in the quotient stack. Currently, we are unable to handle the case that $A^G$ is complete Noetherian local yet.
With Jarod Alper and Jack Hall.
arXiv
Jarod's talk on our result (video)
Grothendieck's existence theorem for relatively perfect complexes on algebraic stacks
I extend Lieblich's algebraization result for complexes on algebraic spaces to the setting of algebraic stacks.
arXiv
Algebraization theorems for coherent sheaves on stacks
My Ph.D. thesis. It is essentially an integrated version of the two papers above.
PDFGeometric Invariant Theory
Moduli functors, GIT and semistability of the gradient morphism for ternary forms
My undergraduate thesis. I generalize a result of Alper and Isaev on the semistability of the gradient morphism from the case of binary forms to cubics forms of degree $d$, for $3 \leq d \leq 9$.
A year or so after I graduated, Fedorchuk generalized my result to arbitrary forms of any
degree. See Theorem 1.4.1 here and
the paragraph below it acknowledging my work.
My undergraduate thesis is available on request.
Notes and Expository Articles
Algebraic Geometry, Arithmetic Geometry and Number Theory
The rank of $y^2 = x^3 - 2$ via Mazur-Tate methods
Inspired by the paper Points of order $13$ on elliptic curves, I show that the rank of the elliptic curve $y^2 = x^3 - 2$ is $1$ using the method of $2$-descent.
PDF
The Picard number of a Kummer surface
I give a self-contained proof that the Picard number of the Kummer surface $X$ associated to an abelian surface $A$, satisfies $\rho(X)= 16 + \rho(A)$.
PDF
A proper scheme with infinite-dimensional fppf cohomology
It is a fundamental fact in étale cohomology that the cohomology of any constructible sheaf on a proper scheme is finite. In this article, I give an example showing this is false in the fppf topology.
PDF Blog article on Thuses
The étale cohomology of curves over a finite field
I compute the étale cohomology (with coefficients in $\mathbf{G}_m$) of a curve over a finite field. The calculation is more subtle than the case over an algebraically closed field, because theorems such as Artin vanishing and Poincaré duality cannot be applied.
Blog article on Thuses
Semicontinuity of weights
Notes for a lecture I gave during the 2016-2017 edition of Stanford's Number Theory Learning Seminar. Given a variety over a finite field, I prove that the weight of a lisse sheaf (in the sense of Deligne) is invariant under restriction to a dense open.
PDF Version on learning seminar website (My notes start from page 9)Representation Theory
The Peter-Weyl theorem
Essay I wrote for the 2013 edition of ANU's Analysis 3 (Functional Analysis and Spectral Theory). I prove the "analytic" version of the Peter-Weyl Theorem, namely that the matrix coefficients of a compact Lie group $G$ are dense in $L^2(G)$.
PDF
Schur-Weyl duality and irreducible representations of $\mathfrak{sl}_n$
Essay I wrote for the 2012 edition of ANU's Algebra 3 (Lie Groups and Lie Algebras). I prove Schur-Weyl duality for $\mathrm{SL}_n(\mathbf{C})$, and using this I deduce the characters and dimensions of the highest weight representations of its Lie algebra.
PDFPast Projects
COVID-19
During the start of the total lockdown in Malaysia on 1/6/2021, I became interested in trying to understand the spread of COVID-19 in Malaysia.
The failure of the 2021 FMCO
I argue that the failure to stop workplace clusters from happening was why the 2021 FMCO failed in the Klang Valley, Johor, Pulau Pinang and Negeri Sembilan. Please see this pdf here. In addition, please see this press statement (with IDEAS and Bait Al-Amanah), urging the federal government to address this issue ASAP.
2021 Bayan Baru Donation Drive
The goal is to raise RM 50,000 (approx. USD 12,000) to be distributed as cash to B40 families around the area of Bayan Baru, Penang, Malaysia during the 2021 FMCO (Full Movement Control Order). The GIVE.asia page to donate is here. This project is joint with the member of parliament for Bayan Baru, YB Sim Tze Tzin.
Education
Ph.D. in Mathematics, Stanford University, 2015-2020.
Ph.B. in Mathematics, Australian National University, 2011-2014.
Honors
University Medal, Australian National University, 2014.