Eric Canton

Mathematician • Staff Engineer & Data Scientist at Arcascope

I work as an engineer of scientific software. My background is in mathematical analysis of many kinds-- I have published four peer-reviewed papers in algebraic geometry and commutative algebra, and am a core author of numerous scientific software packages and apps at Arcascope. I enjoy extracting trends and studying dynamics of data.

Find/contact me:

GitHub

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.

Berkovich log discrepancies in positive characteristic

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).

A note on injectivity of Frobenius on local cohomology of global complete intersections

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.

On the behavior of singularities at the F -pure threshold

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.