**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, 13:00--14:30 in Rio (this is 11:00--12:30 EST, 17:00--18:30 Roma / Paris, 21:30--23:00 Calcutta).

**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**

31/08 | Monoid schemes (Samarpita Ray) <slides> |
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07/09 | Introduction to toric varieties (Oliver Lorscheid) <slides> / Monoid schemes from toric varieties I (Samarpita Ray) <slides> |

21/09 | Monoid schemes from toric varieties II (Samarpita Ray) <slides> |

28/09 | Semiring schemes I (Oliver Lorscheid) <slides> |

05/10 | Semiring schemes II (Oliver Lorscheid) |

12/10 | Kajiwara-Payne tropicalization I (Trevor Gunn) <slides> |

19/10 | Kajiwara-Payne tropicalization II (Trevor Gunn) |

26/10 | Giansiracusa tropicalization (Stefano Mereta) <slides> |

02/11 | Ordered blue schemes I (Manoel Jarra) <slides> |

09/11 | Ordered blue schemes II (Manoel Jarra) <slides> / Tropicalization as a base change I (Hernán Iriarte) <slides> |

16/11 | Tropicalization as a base change II (Hernán Iriarte) <slides> |

23/11 | Tropical ideals (Diane Maclagan) |

30/11 | Algebraic K-theory and Grothendieck-Witt theory of monoid schemes (Matthew B. Young) <slides> |

07/12 | Toric Hall algebras and infinite-dimensional Lie algebras (Matthew Szczesny) <slides> |

14/12 | Problem session |

Here is the initial description of the program, including a reference list.