Eric C. Peterson

I am a mathematician and programmer, working in some intersection or another or these two fields. Presently, I'm working on quantum compilation at AWS; previously, I've worked on active learning as an OpenAI Fellow, on quantum compilation at IBM Research and at Rigetti Computing, and on (chromatic) homotopy theory in academia. In addition to "traditional" research, I am very interested in communication within scientific circles. In particular, I spent a lot of time as an academic coaxing my topologist peers to speak the language of number theory.

My tour in academia consisted of a Benjamin Peirce fellowship in the Harvard math department, graduate work at Berkeley under Constantin Teleman, and undergraduate studies in computer science at Urbana-Champaign under Matt Ando and Elsa Gunter.

This URL used to host a group research blog, Chromotopy.

Writing

My mathematical interests are in using algebro-geometric tools to answer questions in algebraic topology, and I have a penchant for computations—but I've done some other things too.

Papers

Expository writing

I passed my qualifying exam on November 23rd, 2011. Here are my qual syllabus and transcript of the exam questions I could remember.

Here is an unedited copy of my PhD thesis. Beware: this document contains several significant errors. Readers should consult the published version for the original research and the book project for the exposition. A long time ago, I wrote an undergraduate thesis under Elsa Gunter, where we explored a modification of ambient process calculi. Unfortunately, the main technical result remains unfinished.

I'm not very active, but I have also written some things on MathOverflow.

Also, here are two animations of the stabilization of the unstable Adams spectral sequence for the sphere, at the prime 2 and at the prime 3, due to Barnes, Poduska, and Shick.

Speaking

I've given a good number of talks, and I was often funded through a teaching position. Students and onlookers can find both talk notes and course pages below.

Slides, talk notes, reports

Courses / sections taught

Software

monodromy: A small computer algebra system for manipulating polytopes, particularly those related to quantum information theory.
dTQEC: A family of Common Lisp software packages used to implement and analyze Fowler's program for manipulating logical defect qubits.
quilc: A retargetable compiler for gate-based quantum computers. Part of Rigetti's Forest SDK.
Atlas: A real-time, collaborative "mind-mapping" program, designed to be useful for storing a mathematical research program. Here is a public Atlas server, as well as a video demoing its features.
Ext Chart: A utility in development for OS X, useful for drawing and computing with spectral sequences.
Op[]: A rewrite system in Mathematica to determine the closure of a set of cohomology classes in H^*(K(Z, n); Z/2) under the action of the Steenrod algebra. Useful for expanding Singer's and Stong's calculations of H^*(BU<2k>; Z/2).
Coact: Mathematica package for computing the free and square-zero parts of the coaction of the dual Steenrod algebra on the space of multiplicative k-variate cocycles.
A-cocycles: Mathematica package for computing the space of additive cocycles, along with some of the tertiary invariants described in our paper.
A-visual: Mathematica notebook with some graphical routines, displaying some of the tertiary invariants in our paper. Used in a presentation to Stephen Wolfram.
M-cocycles: Mathematica package for computing obstructions to free extension from the tangent space of multiplicative cocycles to the total space. Doesn't completely work, but it's close, and it's complete enough to warrant sharing. Missing backtracking, mostly.
Persistent Sullivan models: Mathematica package for computing the Sullivan minimal model associated to the Vietoris-Rips space built from a point cloud. Supposed to be useful for computing rational 'persistent homotopy groups' of complexes rather than the usual persistent homology groups. This is very slow (in an irreparable way: computing rational homotopy groups has a very high complexity lower bound) and also mildly incorrect, but the slowness has made it hard to debug. Caveat user. (This was part of a project with Matthew Pancia.)
Swift-Agenda: A re-implementation of Agenda as a Swift application, with both iOS and macOS embodiments, networked against a remote backend.
Agenda: A small agenda program, written in OCaml, to keep track of deadlines and so forth, though its feature list has grown marginally from those beginnings. The original to Swift-Agenda.
Smithy: A map editor, also written in OCaml, for the Marathon engine, a game from the mid '90s now actively developed under the name Aleph One.
MW2: A small collection of thoughts on reverse-engineering some of the engine and data pieces in Activision's classic MechWarrior 2.

This is a work in progress.