Computational complexity of polynomial identities

Project Description

Polynomial identities in associative algebras have been a major object of study, as they are a natural generalization of commutative polynomial rings. While the basic structural theory of such rings is somewhat understood, the computational aspects of polynomial identities is still rudimentary. The goal of this project is to study the computational complexity of known polynomial identities and provide, through the computational lens, a systematic study and possibly new polynomial identities based on ideas from algebraic complexity theory. Another goal of this project is to use the better understanding of polynomial identities to solve open problems in non-commutative algebraic complexity theory.

Prerequisites

The ideal URA should already have a solid command of:

• linear algebra (equivalent of MATH 245, or MATH 235),
• basic abstract algebra (such as the material from PMATH 347),
• combinatorics
• be fairly comfortable writing rigorous proofs.

Programming experience is a plus as experiments are part of the project. We will be using Macaulay 2 for computational experiments.

Applying

If you are interested and have the prerequisites for this project, please send me the following by email:

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