Curtis Bright

Postdoctoral Researcher
University of Waterloo
DC 2302G
cbright

Presently, I am working on applying SAT solvers and computer algebra systems to problems in combinatorics and number theory, working with Vijay Ganesh and Ilias Kotsireas. Our work in this area has been published in the Journal of Automated Reasoning, at Computer Algebra in Scientific Computing, at the AAAI Conference on Artificial Intelligence, and will be published at the upcoming International Symposium on Symbolic and Algebraic Computation.

In March 2017, I defended my PhD thesis, supervised by Vijay Ganesh and Krzysztof Czarnecki.

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.

Previously, I delivered tutorials and assisted running courses with a focus on data structures, algorithms, and logic, receiving an award for exceptional TA performance in Spring 2013. I spent most of the decade prior to 2014 becoming well-versed in mathematics: I have taken over 50 courses offered by the Faculty of Mathematics at the University of Waterloo, and have been a teaching assistant or instructor for over 20 courses. My CV contains a summary of my academic career.

**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 also been awarded 0x$1.20 at Knuth's Bank of San Serriffe.

Things I've (co-)written which are available online.

- May 14, 2018 Enumeration of Complex Golay Pairs via Programmatic SAT
- March 19, 2018 Applying computer algebra systems and SAT solvers to the Williamson conjecture [bib]
- March 4, 2018 A doubling construction for Williamson matrices [bib]
- February 4, 2018 A SAT+CAS method for enumerating Williamson matrices of even order poster
- November 20, 2017 A SAT+CAS method for enumerating Williamson matrices of even order [bib]
- November 19, 2017 A new form of Williamson's product theorem [bib]
- July 11, 2017 A SAT+CAS method for enumerating Williamson matrices of even order (preprint)
- April 27, 2017 Computational methods for combinatorial and number theoretic problems [bib, errata]
- December 9, 2016 New results on complex Golay pairs [bib]
- November 19, 2016 Combining SAT solvers with computer algebra systems to verify combinatorial conjectures [bib]
- January 17, 2016 MathCheck2: A SAT+CAS verifier for combinatorial conjectures [bib]
- September 27, 2014 Minimal elements for the prime numbers [bib]
- April 10, 2014 Exceptional examples in the
`abc`conjecture [bib] - April 15, 2013 Computing the Galois group of a polynomial [bib]
- April 21, 2012 The quartic formula derivation [bib]
- April 21, 2012 The quartic formula poster
- April 2, 2012 8*13^(4*8005)+183 is a probable prime
- December 29, 2011 From the shortest vector problem to the dihedral hidden subgroup problem [bib]
- April 20, 2011 Passing arguments: A comparison among programming languages [bib]
- April 9, 2011 Vector rational number reconstruction poster
- March 30, 2011 Vector rational number reconstruction [bib, errata]
- December 20, 2010 Automated construction of phylogenetic trees [bib]
- December 13, 2010 Ataxx with AI
- August 31, 2009 Vector rational number reconstruction
- April 29, 2009 Reduction of lattice bases [bib]
- April 16, 2009 Neural networks for insurance fraud detection [bib]
- December 15, 2008 Algorithms for lattice basis reduction
- July 20, 2008 Notes on chapter 2 of Ideals, Varieties and Algorithms
- April 24, 2008 Modular periodicity of linear recurrence sequences
- April 18, 2008 Insurance fraud statistics
- February 12, 2008 Solving Ramanujan's square equation computationally [bib]
- February 12, 2008 NSRA on Obláth's problem
- September 12, 2007 Finding generalized near-repdigit squares

Talks I've given which used slides.

- February 4, 2018 A SAT+CAS Method for Enumerating Williamson Matrices of Even Order AAAI, New Orleans, USA
- July 29, 2017 A SAT+CAS Method for Enumerating Williamson Matrices of Even Order SC
^{2}Workshop, Kaiserslautern, Germany - March 23, 2017 Computational methods for combinatorial and number theoretic problems
- December 7, 2016 MathCheck2: A SAT+CAS verifier for combinatorial conjectures
- December 7, 2016 Minimal elements for the prime numbers
- November 18, 2016 MathCheck2: A SAT+CAS verifier for combinatorial conjectures
- September 24, 2016 MathCheck2: Combining learning-based search (SAT) with symbolic computation (CAS) SC
^{2}Workshop, Timişoara, Romania - September 20, 2016 MathCheck2: A SAT+CAS verifier for combinatorial conjectures CASC, Bucharest, Romania
- July 12, 2016 MathCheck: A math assistant combining SAT with computer algebra systems IJCAI, New York, USA
- July 2, 2016 MathCheck2: A SAT+CAS verifier for combinatorial conjectures SMT Workshop, Coimbra, Portugal
- May 13, 2016 MathCheck2: A SAT+CAS verifier for combinatorial conjectures ACMES, London, Ontario
- March 14, 2016 PhD Research Proposal: A SAT+CAS system for checking math conjectures
- March 27, 2014 Extremal examples in the
`abc`conjecture - September 9, 2013 Proving the Prime Number Theorem in an hour
- April 8, 2013 Computing the Galois group of a polynomial
- December 8, 2011 From the shortest vector problem to the dihedral hidden subgroup problem
- June 9, 2011 Vector rational number reconstruction ISSAC, San Jose, USA
- August 28, 2009 Vector rational number reconstruction: Version 2
- August 20, 2009 Vector rational number reconstruction
- May 21, 2009 Lattice basis reduction and the LLL Algorithm
- July 31, 2008 LLL overview: Lenstra-Lenstra-Lovász lattice basis reduction
- July 3, 2008 Notes on chapter 2 of Ideals, Varieties and Algorithms

I use LaTeX for taking notes. How well this works depends on the course content; it typically works better in pure mathematics courses than in computer science courses. Although I can't guarantee the accuracy or completeness of my transcriptions, I'm posting some notes for courses I've taken (or sat through) in the hope they will be useful to others. Let me know if you spot any typos, or even better, fix them yourself on GitHub.

- PMATH 641 Winter 2013 Algebraic Number Theory with Cameron Stewart
- PMATH 740 Spring 2012 Analytic Number Theory with Stephen New
- PMATH 442 Fall 2011 Galois Theory with David McKinnon
- PMATH 345 Spring 2010 Polynomials, Rings and Finite Fields with David McKinnon
- PMATH 351 Winter 2010 Real Analysis with Che Tat Ng
- PMATH 345 Fall 2009 Polynomials, Rings and Finite Fields with Rahim Moosa
- PMATH 351 Fall 2009 Real Analysis with Kathryn Hare
- PMATH 944 Fall 2009 Geometry of Numbers with Cameron Stewart

I was the designer of the SCG logo, a spoof on a proposed UW logo. Other nonacademic projects of mine can be found on my personal website, www.curtisbright.com.