Eric Canton

Mathematician Engineering & Data at Arcascope

As senior engineer and data scientist at Arcascope, I spend my time leading initial research and development of new software and data applications and providing mentorship to newer members of our engineering team. I like to think about data systems engineering, optimal control, symplectic geometry, topological data analysis, and differentiable programming.

My most significant projects include:

  • designing and authoring the API and backend services for the first clinical trial of Arcascope's algorithms, and collaborating with another data scientist to integrate existing mathematical software into this backend.

  • co-authoring our circadian modeling and optimzation package, central to our circadian health technology.

  • initial development of an iOS and Apple Watch app implementing actigraphy on the Watch, and cloud persistence of health statistics.

  • one of four initial developers on Arcascope's Shift app.

  • selecting technologies for our data lakehouse, designing and implementing the ETL and weekly batch reports of this data, using Apache Spark on AWS Glue.

  • development of a machine learning research package investigating sleep prediction using consumer wearables data.

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. I then spent six months at Enel X North America interning as a software engineer, where I worked on a team developing and maintaining an energy market modeling package and web UI, written in R.


Find/contact me:

GitHub

LinkedIn

Portfolio

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 Trulia.com.

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

https://dx.doi.org/10.4310/PAMQ.2020.v16.n5.a5

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

https://doi.org/10.1016/j.jpaa.2016.01.006

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

https://doi.org/10.1215/ijm/1506067286

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.

Contact me at eric.d.canton@gmail.com