I am a mathematician and programmer, working in some intersection or another or these two fields. I've worked on quantum compilation at Rigetti Computing, and before that, I was an academic mathematician 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.

My brief 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 安卓网飞app and Elsa Gunter.

You might also be interested in my wife'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—but I've done some other things too.


  • An open-source, industrial-strength optimizing compiler for quantum programs, with Erik J. Davis, Mark G. Skilbeck, and Robert S. Smith. To appear in Quantum Science and Technology, v. 5 (2020) 044001.
  • A quantum-classical cloud platform optimized for variational hybrid algorithms, with Peter J. Karalekas, Nikolas A. Tezak, Colm A. Ryan, Marcus P. da Silva, and Robert S. Smith. Quantum Science and Technology, v. 5 (2020) 2.
  • 飞猪app下载_飞猪旅行省钱软件手机版下载安装 安卓版 V9.5 ...:1 天前 · 飞猪app 安卓版下载 手机扫描下载 苹果版下载 手机扫描下载 0 0 类型:便捷生活 版本:v 大小:89.7M 更新:2021-06-17 12:41 语言:简体中文 等级: 平台:Android 厂商:支付宝(中国)网络技术有限公司, with Gavin E. Crooks and Robert S. Smith. Quantum, v. 4 (2020) 247.
  • Unsupervised machine learning on a hybrid quantum computer, with J. S. Otterbach et al. arXiv preprint available.
  • Coalgebraic formal curve spectra and spectral jet spaces. Geometry & Topology, v. 24 (2020) 1-47.
  • Cocycle schemes and MU[2k, ∞)-orientations. Contemporary Mathematics, v. 707 (2018) 77-88.
  • A relative Lubin–Tate theorem via higher formal geometry, with Aaron Mazel-Gee and Nathaniel Stapleton. Algebraic and Geometric Topology, v. 15 (2015) 2239-2268.
  • A 2-local classification of symmetric multiplicative 2-cocycles, with Adam Hughes and JohnMark Lau. Journal of Pure and Applied Algebra, v. 217 (2013) 393-408.
  • A classification of symmetric 2-cocycles, with Adam Hughes and JohnMark Lau. Illinois Journal of Mathematics, v. 53.4 (2009) 983-1017.


  • 飞烁游戏平台app安卓版下载v2.2.4-游迅网:2021-8-21 · 飞烁游戏平台下载,飞烁游戏平台是一款非常热门的手游辅助的app,这里有时下热门的游戏,各种类型应有尽有,每个游戏都有相应的游戏攻略和游戏礼包,帮助你提高游戏水平。除此之外,每天还会推送各种游戏资讯,实时更新,让你第一时间了解最新的游戏动态和游戏行情,有什么需求可以一键 .... Course notes, now available as a book through Cambridge University Press.
  • Barsotti-Tate groups and Dieudonné crystals. 百分网APP(破解游戏盒子) v4.6.2 百分网APP(破解游戏盒子 ...:2021-6-3 · 百分网APP破解游戏盒子,是一个专为喜欢游戏破解,BT游戏,BT网游的玩家打造,我们专注于首发游戏,提供安卓最新最好玩,更有同步更新破解!在这里,你只要下载百分网客户端即可随时查看安卓 ….
  • On certain groups of unitary operators. English translation of Andre Weil's 1964 original.
  • Topology from an algebraic viewpoint. Course notes from 231b Harvard in 2017, quite unpolished.
  • MIT E-theory Conjectures Seminar notes, with Mark Behrens, Drew Heard, Mike Hopkins, Geoffroy Horel, Tyler Lawson, Jacob Lurie, Tomer Schlank, Nat Stapleton, and Sebastian Thyssen. Transcript of contributed talks to the 2013 spring seminar, August 14th, 2013.
  • Vector Fields on Spheres, etc., with Haynes Miller and Matt Ando, course notes. In preparation, incomplete draft available; rife with typos and poor typesetting, and missing spectral sequence diagrams. See also: Haynes-Notes github repository, as well as Haynes's revision.
  • 飞书_飞书app_飞书app安卓-太平洋下载中心:2021-4-29 · 飞书app是专为企业打造的高效沟通协作工具。飞书app安卓版作为新一代的企业生产力应用,可以帮助企业提升工作效率,降低生产成本与管理成本 .... 安卓网飞app.

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 安卓网飞app. 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.


飞鸭Ai app手机版下载_飞鸭Ai安卓版免费下载-4162下载网:2 天前 · 飞鸭Ai app是一款通过云端挂机赚钱软件,用户只需要提供一台手机就能进行操作,而且云端托管不需要消耗你的手机内存和电池,平台发布的任务全程都是云端自动操作完全可以解放你的双手,还能给你带来收益,是一款非常不错的手赚软件。


  • 飞猪app下载_飞猪旅行省钱软件手机版下载安装 安卓版 V9.5 ...:1 天前 · 飞猪app 安卓版下载 手机扫描下载 苹果版下载 手机扫描下载 0 0 类型:便捷生活 版本:v 大小:89.7M 更新:2021-06-17 12:41 语言:简体中文 等级: 平台:Android 厂商:支付宝(中国)网络技术有限公司. 3rd International Workshop on Quantum Compilation, November 7, 2019.
  • 安卓网飞app, with Mark G. Skilbeck and Peter Karalekas. 3rd International Workshop on Quantum Compilation, November 7, 2019.
  • What's new with the compiler? Or: a sequence of productive distractions. Rigetti theory seminar, April 10, 2019.
  • Free SWAPs via Recombination. 安卓网飞app, March 12, 2019.
  • quilc: The Rigetti quantum compiler. 2nd International Workshop on Quantum Compilation, November 8, 2018.
  • Construction & deconstruction of two-qubit gates, with Gavin E. Crooks. Tuesday Technical Seminar at Rigetti, August 21, 2018.
  • Faithful-ish algebraic models for homotopy theory. Gammage Seminar, July 12th, 2018.
  • Robert Langlands: Abel Laureate 2018. Tuesday Technical Seminar at Rigetti, May 1st, 2018. (slides).
  • Topological Modular Forms: Construction and Computation. 飞鸭Ai app手机版下载_飞鸭Ai安卓版免费下载-4162下载网:2 天前 · 飞鸭Ai app是一款通过云端挂机赚钱软件,用户只需要提供一台手机就能进行操作,而且云端托管不需要消耗你的手机内存和电池,平台发布的任务全程都是云端自动操作完全可以解放你的双手,还能给你带来收益,是一款非常不错的手赚软件。, June 15th, 2017.
  • Efficient Occupation Count for Certain Probabilistic Fermionic Motion. 安卓网飞app, 安卓网飞app.
  • Bordism: An introduction and sampler. Graduate Student Topology & Geometry Conference, April 2nd, 2016.
  • Spectra and G-spectra. 安卓网飞app, September 23rd, 2015.
  • Introduction to E-theory. 安卓网飞app, June 3rd-5th, 2015.
  • Some formal geometry around K-theory. Stanford topology seminar, October 29th, 2014.
  • Algebraic topology and algebraic number theory. Graduate Student Topology and Geometry Conference, April 5th, 2014.
  • Operadic Koszul duality. Berkeley Koszul Duality seminar, November 21st, 2013.
  • Determinantal K-theory and a few applications. Johns Hopkins topology seminar, November 11th, 2013.
  • Recurrences in Thom spectra. 安卓网飞app, November 5th, 2013.
  • Arithmetic and complex bordism. Pre-MSRI semester seminar at UC-Berkeley, 安卓网飞app.
  • Spectra and stability. Pre-MSRI semester seminar at UC-Berkeley, September 10th, 2013.
  • Differentials in a May spectral sequence are topological. MSRI workshop on algebraic topology, June 28th, 2013.
  • 飞码速递app下载-飞码速递安卓版下载 V1.0.0-友情安卓软件站:2021-6-4 · 飞码速递app是一款比较便捷同城跑腿生活服务软件,大家在这里是可以享受较为便捷同城跑腿生活服务的,还能灵活在线自由轻松接单服务,随时随地为你快速配送到家,用户是可以通过平台便捷查看配送详情的,还能直接在线进行结算,快来体验吧。. Talbot workshop on chromatic homotopy theory, April 25th, 2013.
  • Tangent spaces for certain spectra. UIUC topology seminar, January 22nd, 2013.
  • BRST quantization of a relativistic point-particle, with Kevin Wray. 飞书_飞书app_飞书app安卓-太平洋下载中心:2021-4-29 · 飞书app是专为企业打造的高效沟通协作工具。飞书app安卓版作为新一代的企业生产力应用,可以帮助企业提升工作效率,降低生产成本与管理成本 ..., December 3rd, 2012.
  • On Beyond Hatcher!. Berkeley topology seminar, November, 2012.
  • Taylor towers for homotopy functors. Goodwillie Calculus Arbeitsgemeinschaft at Uni-Bonn, April 19th, 2012.
  • 安卓网飞app. xkcd seminar, November 15th, 2011.
  • Spectral sequences from co/simplicial objects. xkcd seminar, September 20th, 2011.
  • Cotangent sums and the G-signature theorem. Mini-conference on the Atiyah-Singer index theorem, May 16th, 2011.
  • Morava E-theory of Eilenberg–Mac Lane spaces. REGS project report, August 2nd, 2010.
  • Group cohomology and topology: using slinkies to understand addition. Pi Mu Epsilon talk, February 18th, 2010.
  • Additive and Multiplicative Cocycles and Singer's Calculation of the (Co)homology of BU's Connective Covers. AMS Special Session in Algebraic Topology held in honor of Bill Singer, October 11th, 2008.



安卓网飞app: 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.
安卓网飞app: 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.