What can topology tell us about the neural code?

TL;DR

This paper explores how topological methods can be applied to understand neural codes, highlighting recent advances and the natural fit of topology for analyzing neural data.

Contribution

It surveys recent applications of topology in neuroscience and explains why topological tools are particularly suitable for studying neural coding.

Findings

Topological methods reveal structure in neural data

Topology provides insights into neural coding mechanisms

Recent applications demonstrate the utility of topology in neuroscience

Abstract

Neuroscience is undergoing a period of rapid experimental progress and expansion. New mathematical tools, previously unknown in the neuroscience community, are now being used to tackle fundamental questions and analyze emerging data sets. Consistent with this trend, the last decade has seen an uptick in the use of topological ideas and methods in neuroscience. In this talk I will survey recent applications of topology in neuroscience, and explain why topology is an especially natural tool for understanding neural codes. Note: This is a write-up of my talk for the Current Events Bulletin, held at the 2016 Joint Math Meetings in Seattle, WA.