Applications of algebra, geometry, and combinatorics to spatial navigation

Abstract: There are three types of cells involved in spatial navigation: place cells, grid cells, and head direction cells. Place cells fire every time an animal is in a specific location, grid cells fire in a repeating sequence as the animal travels along particular trajectories, and head direction cells indicate the way an animal is facing. While many people study these using mathematical modeling and more traditional applied mathematics techniques, there is a growing community of people using algebraic, geometric, and combinatorial tools to analyze place and grid cells. In this talk I'll discuss how I use combinatorial commutative algebra to study place cells (building on work of Curto, Itskov, et al) and geometry to study grid cells. The work on place cells is joint with Hugh Geller, Alexandra Seceleanu, and Nora Youngs, and the work on grid cells is joint with Giorgio Ascoli, Holger Dannenberg, Kelsi Listman, Nate Sutton, and Anthony Vu.

algebraic geometrycombinatorics

Audience: researchers in the discipline

MAAGC 2026

Series comments: The 2026 annual Mid-Atlantic Algebra, Geometry, and Combinatorics (MAAGC) Workshop will take place October 23-25, 2026, at VCU.

The MAAGC Workshop aims to bring together senior researchers and junior mathematicians from the region to exchange ideas and forge collaborations in algebra, geometry, and combinatorics. The conference is funded by National Science Foundation grant DMS-2408985.