- Series
- Algebra Seminar
- Time
- Monday, September 19, 2022 - 1:30pm for 1 hour (actually 50 minutes)
- Location
- Clough 125 Classroom
- Speaker
- Matt Baker – Georgia Institute of Technology – mbaker@math.gatech.edu – https://sites.google.com/view/mattbakermath/home/
- Organizer
- Papri Dey

I will give an introduction to Oliver Lorscheid’s theory of ordered blueprints – one of the more successful approaches to “the field of one element” – and sketch its relationship to Tits models for algebraic groups and moduli spaces of matroids. The basic idea for these applications is quite simple: given a scheme over Z defined by equations with coefficients in {0,1,-1}, there is a corresponding “blue model” whose K-points (where K is the Krasner hyperfield) sometimes correspond to interesting combinatorial structures. For example, taking closed K-points of a suitable blue model for a split reductive group scheme G over Z gives the Weyl group of G, and taking K-points of a suitable blue model for the Grassmannian G(r,n) gives the set of matroids of rank r on {1,...,n}.