### Max-Intersection Completeness of Neural Codes and the Neural Ideal

- Series
- Algebra Seminar
- Time
- Monday, January 22, 2024 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Alexander Ruys de Perez – Georgia Tech

**Please Note:** There will be a pre-seminar (aimed toward grad students and postdocs) from 11:30 am to noon in Skiles 005.

A neural code C on n neurons is a collection of subsets of {1,2,...,n} which is used to encode the intersections of subsets U_1, U_2,...,U_n of some topological space. The study of neural codes reveals the ways in which geometric or topological properties can be encoded combinatorially. A prominent example is the property of max-intersection completeness: if a code C contains every possible intersection of its maximal codewords, then one can always find a collection of open convex U_1, U_2,..., U_n for which C is the code. In this talk I will answer a question posed by Curto et al. (2018), which asks if there is a way of determining max-intersection completeness from examination of the neural ideal, an algebraic counterpart to the neural code.