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.
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.
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.