Headshot of Curtis
Curtis Bright Postdoctoral Researcher
cbright

I work on developing efficient search algorithms to solve mathematical problems through satisfiability checking and computer algebra. I am currently the lead developer of the MathCheck project at the University of Waterloo. In 2020, I am holding an NSERC postdoctoral fellowship at Carleton University working with professors Kevin Cheung and Brett Stevens. See my curriculum vitae or bio for a summary of my academic career and my research statement or publication list for an overview of my research.

Bragging rights: My Erdős number is 2, through the papers Minimal elements for the prime numbers (Bright, Devillers, Shallit) and New bounds on the length of finite Pierce and Engel series (Erdős, Shallit). I have been awarded 0x$1.20 at Knuth's Bank of San Serriffe for finding a typo in The Art of Computer Programming present since the first edition (!) of volume 2 in 1969. In the 2015 version of his classic text Galois Theory, Ian Stewart cited a report of mine. Additionally, Noam Elkies once gave a talk referencing a result that I showed as an undergraduate student—the technical report is dear to my heart as one of the first papers I ever wrote.

Published Works

My work has been published in a number of notable venues including in the Journal of Automated Reasoning 2017, at the AAAI Conference on Artificial Intelligence 2018 (and 2019), at ISSAC 2018 (and 2011), at CASC 2016, at CASCON 2019, in the Journal of Experimental Mathematics 2016, in the Journal of Symbolic Computation 2019 (and again in 2019) and in the Annals of Mathematics and Artificial Intelligence 2019. In 2020, my work will appear in Applicable Algebra in Engineering, Communication and Computing and in a chapter of the book Maple in Mathematics Education and Research. Most of the articles are behind paywalls but preprints for each of my papers are available below if you do not have access through the publisher's site.

Writings

Copies of my academic writings in reverse chronological order. The oldest are technical reports written during my undergraduate studies and I have archived them here as a part of my long-term commitment to improve my writing.

Showcase

Apps and posters that I've written to showcase my research and some of its applications. I enjoy bringing life to my research by using accessible visualizations and interactivity.

Colouring of the 8x8 queens graph Graph Colouring with SAT September 9, 2019
15-puzzle instance Solving the 15-puzzle December 19, 2018
Completed Sudoku puzzle Interactive Sudoku December 3, 2018
Highlighted clique of size 4 in a graph with 20 vertices Clique Finding with SAT November 15, 2018
Graeco-Latin square of order 10 Finding Graeco-Latin Squares November 7, 2018
Solution of the 8-Queens problem The n-Queens Problem October 4, 2018
Einstein with the text 'Who owns the fish?' Solving the Einstein Riddle October 4, 2018
Ataxx gameplay example Ataxx AI November 15, 2012
The quartic formula (cropped) The Quartic Formula [webpage] April 21, 2012

Talks

An archive of my academic talks that have used slides.

Bio

I am currently working on the MathCheck project run by professor Vijay Ganesh of the University of Waterloo while based at Carleton University working with professors Kevin Cheung and Brett Stevens. I am also affiliated with Wilfrid Laurier University working with professor Ilias Kotsireas.

I interned at Maplesoft in 2017 and again in 2018. While at Maplesoft I applied my research to dramatically improve some discrete optimization routines of Maple—for example, in the latest version of Maple the chromatic number of the Queen Graph of the chessboard can be computed in a few seconds instead of a few hours. I have written a number of Maple applications demonstrating how to effectively use Maple's SAT solver in a variety of problems.

In March 2017, I defended my PhD thesis, supervised by Vijay Ganesh and Krzysztof Czarnecki. My thesis demonstrated the effectiveness of combining satisfiability checking and symbolic computation for solving mathematical problems.

In Fall 2015, I taught Elementary Algorithm Design and Data Abstraction alongside Gordon Cormack to 258 students. This course is the follow-up to Designing Functional Programs intended for CS and math majors and uses the programming language C.

In Summer 2015, I was the sole instructor of 145 students in Introduction to Computer Science 1, an introduction to computer science intended for non-CS majors. As the instructor I was responsible for compiling 9 assignments throughout the term and each one consisted of questions newly developed by myself.

In Fall 2014, I taught Designing Functional Programs, an introduction to computer science for CS and math majors based around the programming language Racket. I coordinated with 5 other instructors to teach 876 students.

In Summer 2014, as a part of Google's summer of code I supervised (along with William Hart) the undergraduate student Abhinav Baid and oversaw the implementation of a fast variant of the LLL algorithm for lattice basis reduction in the open source number theory library FLINT. This code is available in the latest version of FLINT in the fmpz_lll module.

In Spring 2013, I received an award for exceptional performance as an instructional assistant in the course Logic and Computation. During this term I wrote an online truth table generator for easily generating truth tables to include in assignment solutions and course notes.

In Winter 2013, I designed the SCG logo (a spoof on a proposed UW logo). At the time I was a graduate student and I've made publicly available a collection of the lecture notes that I took as a student.

In 2007, I started a personal website for nonacademic projects, though most of my effort these days goes into advancing my research program.