Palmer Mebane
Thesis
Uniquely Solvable Puzzles and Fast Matrix Multiplication
- Advisor
- Michael Orrison
- Second Reader(s)
- Nicholas Pippenger
Abstract
In 2003 Cohn and Umans introduced a new group-theoretic framework for doing fast matrix multiplications, with several conjectures that would imply the matrix multiplication exponent $\omega$ is 2. Their methods have been used to match one of the fastest known algorithms by Coppersmith and Winograd, which runs in $O(n^{2.376})$ time and implies that $\omega \leq 2.376$. This thesis discusses the framework that Cohn and Umans came up with and presents some new results in constructing combinatorial objects called uniquely solvable puzzles that were introduced in a 2005 follow-up paper, and which play a crucial role in one of the $\omega = 2$ conjectures.
Proposal
Fast Multiplication of Arbitrary and Structured Matrices via Group Algebras
