Eric Canton

Mathematician Lead Cloud Developer at Arcascope

I am the lead cloud engineer at Arcascope, where I build data engineering pipelines for cutting-edge mathematical biology models. I also like to think about optimal control, symplectic geometry, and differentiable programming.

Before joining Arcascope, I spent two years as an postdoctoral professor in the mathematics department at the University of Michigan, where I worked in algebraic geometry and commutative algebra.

In Summer 2020 I started transitioning from academia to industry with an internship as a software engineer at Enel X North America. There, I worked with a team developing a solar+storage modeling app in R using the Shiny library.

Currently I run Debian Linux and macOS on my personal machines; I have 8+ years experience using Linux for my primary OS. At work, I develop on macOS.

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Sleep classification CNN

Using a convolutional neural network and short-term Fourier transforms (spectrograms) of accelerometer data, we can distinguish awake from asleep at 85-90% TPR with 60% FPR.

(Joint with Dr. Olivia Walch)

Check it out in Google Colab

Unsupervised clustering of houses for sale

My partner and I moved to Eau Claire, WI and were looking at houses. To better understand the housing market there, I use k-means and OPTICS to segment for-sale house listings I scraped from

The clustering was based on density of nearby venues, and also categories of nearby venues like coffee shops and parks/playgrounds, fetched from Foursquare's REST API.

Check it out on my GitHub

Pure mathematics

My research in pure mathematics is in the intersection of algebraic geometry, commutative algebra, and harmonic analysis.

Pure and Applied Mathematics Quarterly, vol. 16 (2020) no. 5, article 5, pp.1465–1532

Based on PhD Thesis.

Harnessing the powerful theory of Berkovich spaces, I prove a collection of theorems about singular algebraic varieties over positive characteristic fields. Reflecting deep connections between Berkovich spaces and Fourier transforms, I convert difficult bounds on singularities (derivative condition) to linear inequalities on transforms (algebraic condition).

Journal of Pure and Applied Algebra, Vol. 220, Issue 8, August 2016, pp.2879–2885

By giving new, explicit formulae for the Frobenius action on local cohomology of certain kinds of projective varieties, I extend theorems of B. Bhatt and A. Singh relating singularities of these varieties to their cohomological structure. The key idea is to apply the local cohomology functors to graded free resolutions of the varieties' ideals.

Illinois Journal of Mathematics, Volume 60, Number 3-4 (2016), pp.669-685

Joint with Daniel Hernández, Karl Schwede, and Emily E. Witt.

We study new families of varieties where the log canonical and F-pure thresholds do not coincide; these are two numerical measures of singularities that have deep, mysterious connections. We also study a volume called the F-signature whose derivatives I related to other volumetric invariants of singularities as an undergraduate, working with Karl.

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