Oliver Lorscheid
11–12 December 2025
Speaker
- Oliver Lorscheid (University of Groningen)
Location and Schedule
The seminar will be held at Bielefeld University in room M4-122.
| 11 December | |
|---|---|
| 14:00 – 15:00 | $\mathbb{F}_1$-geometry via band schemes I |
| 15:00 – 17:00 | Coffee, Tea, and Discussions |
| 12 December | |
|---|---|
| 10:00 – 11:00 | $\mathbb{F}_1$-geometry via band schemes II |
| 11:00 – 12:30 | Coffee, Tea, and Discussions |
Abstract and background reading
In joint work with Matt Baker and Tong Jin, we introduce band schemes as a streamlined version of previous approaches to $\mathbb{F}_1$-geometry (notably that of ordered blue schemes), which is tailored for applications in tropical scheme theory, matroid theory and algebraic groups over $\mathbb{F}_1$.
In these talks at SEA, I will give an introduction to band schemes and try to connect them to several topics that might be of interest for the SEA group, such as the connection to toric geometry and to tropical geometry, as well as the realization of so-called “$\mathbb{F}_1$-rational” points in this formalism for certain “combinatorially defined” varieties.
The main reference is:
- Matthew Baker, Tong Jin, and Oliver Lorscheid. New building blocks for $\mathbb{F}_1$-geometry: bands and band schemes. J. Lond. Math. Soc. (2) 111 (2025), no. 4, Paper No. e70125, 62 pp.
Complementary references are:
- Oliver Lorscheid. $\mathbb{F}_1$ for everyone. Jahresber. Dtsch. Math.-Ver. 120 (2018), no. 2, 83–116. (An overview paper of $\mathbb{F}_1$-geometry).
- Oliver Lorscheid. Tropical geometry over the tropical hyperfield. Rocky Mountain J. Math. 52 (2022), no. 1, 189–222.
- Manoel Jarra, Oliver Lorscheid, and Eduardo Vital. Quiver matroids – Matroid morphisms, quiver Grassmannians, their Euler characteristics and $\mathbb{F}_1$-points.
Sponsors
The SEA Seminar is generously supported by