**Aim of the course**

In this course, we study some aspect of F1-geometry. We will start with a historical talk and an overview of the Connes-Consani program to prove the Riemann hyptothesis. Then we turn towards studying some basic concepts of F1-geometry, such as monoid schemes, semiring schemes and blue schemes. Finally we turn to applications of these concepts in tropical geometry and matroids theory.

**Schedule**

We can use room 228 on Mondays, 15:30--17:00, and Fridays, 13:30--17:00. The rule is that we meet every Friday for one or two talks, starting at 13:30. But at times, we need to cancel a meeting on Friday or to make use of the Monday slot. All exceptions to the rule are listed below:

3/16 Talk on Monday at 15:30.

**References**

Matt Baker and Oliver Lorscheid. The moduli space of matroids. Preprint, arXiv:1809.03542, 2018.

Alain Connes. An essay on the Riemann hypothesis. In Open problems in mathematics, pages 225-257. Springer, 2016.

Jeffrey Giansiracusa and Noah Giansiracusa. Equations of tropical varieties. Duke Math. J., 165(18):3379-3433, 2016.

Oliver Lorscheid. Scheme theoretic tropicalization. Preprint, arXiv:1508.07949, 2015.

Oliver Lorscheid. F1 for everyone. Jahresber. Dtsch. Math.-Ver. 120(2):83-116, 2018.

Sam Payne. Analytification is the limit of all tropicalizations. Math. Res. Lett., 16(3):543-556, 2009.

More informations soon.