Title: Canonical forms of neural ideals

Abstract: A neural ideal captures the firing pattern of a set of neurons (called a neural code), turning problems in coding theory into algebraic questions. In Curto, Itskov, et al. 2013, the authors gave an algorithm for computing the canonical form of a neural ideal, a unique set of pseudomonomial generators (products of $x_i$ and $1-x_j$) corresponding to the neural code. In Gunturkun, Jeffries, and Sun 2020, the authors gave a technique for polarizing neural ideals, to turn them into monomial ideals while retaining the structure of the canonical form. In joint work with Hugh Geller (Sewanee, The University of the South), we give a simple criterion for determining whether a polarized neural ideal is in canonical form. In order to do this, we examine in detail how the generators of an ideal change throughout the algorithm for computing the canonical form. We also describe the canonical forms of some classes of polarized neural ideals.