**Aim of the course**

In this online seminar, we study some aspect of F1-geometry with a focus on tropical scheme theory. In the first part of the seminar, we will study some basic concepts, such as monoid schemes, blueprints and tropical varieties. There is some flexibility in the choice of some more advanced topics for the later parts of the seminar.

The time of the seminar is Mondays, 12:00--13:30 in Rio (this is 11:00--12:30 EST, 17:00--18:30 Roma / Paris, 20:30--22:00 Calcutta). The date of the first talk is August 31, afterwards we meet on a weekly basis.

**Online access**

The seminar can be entered with Zoom. The ID of the meetings is 968 5662 4592 and the password can be found here.

**Program**

The topics for the upcoming weeks are as follows:

31/8 | Monoid schemes (Samarpita Ray) <slides> |
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7/9 | Introduction to toric varieties (Oliver Lorscheid) <slides> / Monoid schemes from toric varieties I (Samarpita Ray) <slides> |

14/9 | Seminar cancelled! |

21/9 | Monoid schemes from toric varieties II (Samarpita Ray) |

28/9 | Semiring schemes (Oliver Lorscheid) |

5/10 | Kajiwara-Payne tropicalization (Trevor Gunn) |

12/10 | Giansiracusa tropicalization (Stefano Mereta) |

19/10 | Ordered blue schemes (Manoel Jarra) |

26/10 | Tropicalization as a base change (Hernán Iriarte) |

Note that it the future dates are only approximate. It is very likely that some topics will occupy us for more than one session, in which case all subsequent talks start later.

Everybody who wants to contribute to the seminar is very welcome! Here is a description of additional topics, including a reference list. Additional suggestions are also welcome!