About Me

I am a mathematician studying cryptography and verifiable computation. I am currently interested in interactive proof systems, succinct arguments, and zero-knowledge protocols, particularly as they relate to cryptocurrency and distributed blockchain applications. My academic background is in theoretical mathematics in the areas of algebraic combinatorics and commutative algebra, and I am currently a visiting research associate at Colorado State University. I received my PhD in mathematics from U.C. Berkeley in 2018, advised by Olga Holtz.

Writing

I am in the early stages of writing a long-form text about the algorithms and protocols used in zero-knowledge verifiable computation. My goal is to produce a resource that aggregates both concrete statements of algorithms and protocols, and succinct and rigorous proofs of their cryptographic properties. In parallel, I will be writing a Rust library of working implementations for the material covered in the book.

Some of my academic writings are:

  • G. Averkov, A. Chavez, J. De Loera, B. Gillespie. "The Lattice of Cycles of an Undirected Graph." Linear Algebra and its Applications, 611(3), 2020.
  • B. Gillespie. "Convexity in Ordered Matroids and the Generalized External Order." The Electronic Journal of Combinatorics, 27(3):P3.41, 2020.
  • B. Gillespie. "The Generalized External Order, and Applications to Zonotopal Algebra." PhD Thesis, University of California, Berkeley. 2018.

For a complete list of papers and talks, see my CV.

Teaching

I will be teaching a new course, MATH 480: Mathematics of Blockchain Protocols, at Colorado State University in Fall 2022. We will be covering zero-knowledge and verifiable computation protocols and underlying mathematical primitives, using Justin Thaler's book "Proofs, Arguments, and Zero-Knowledge" as a primary text.

An archive of course websites and other resources for my previous teaching as a grad student at U.C. Berkeley can be found here.

Software

Check out my profile on github for most of my software projects. A few older projects from grad school include:

  • Voter Model: an interactive simulation of the voter model, a probabilistic model for opinion dynamics on a graph.
  • Zonotopal Spaces: Sage code for explicitly generating the zonotopal spaces described in Olga Holtz and Amos Ron's 2011 publication "Zonotopal Algebra" and related literature.
  • Tableau Combinatorics: a tool for more easily manipulating Young tableaux and Young diagrams. Also available in English notation.

Contact Me

Email IconBryan.Gillespie@colostate.edu

Twitter Icon@bryan_gillespie

Github Icongithub.com/bgillesp