Eric C. Peterson

I was a Benjamin Peirce fellow in the Harvard math department, but I moved on to work in quantum computing at Rigetti. Back when I was a pure mathematician, I focused on homotopy theory, especially the connections between algebraic topology and algebraic geometry known as "chromatic homotopy theory". In addition to research, I was very interested in the communicative aspects of the field, and I spent a lot of time learning how to coax my topologist peers into speaking in terms of number theory.

Before any of that, I was a graduate student at Berkeley under Constantin Teleman. Before that, I was an undergraduate in computer science at Urbana-Champaign, under Matt Ando and Elsa Gunter.

You might also be interested in my partner's website, ThisIsSam. Also, this URL used to host a group research blog, Chromotopy.


My mathematical interests are in using algebro-geometric tools to answer questions in algebraic topology, and I have a penchant for computations.


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.

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.


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


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.)
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.
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.