Reading course on F1-geometry, 2020

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

31/08Monoid schemes (Samarpita Ray) <slides>
07/09Introduction to toric varieties (Oliver Lorscheid) <slides> /
Monoid schemes from toric varieties I (Samarpita Ray) <slides>
21/09Monoid schemes from toric varieties II (Samarpita Ray) <slides>
28/09Semiring schemes I (Oliver Lorscheid) <slides>
05/10Semiring schemes II (Oliver Lorscheid)
12/10Kajiwara-Payne tropicalization I (Trevor Gunn) <slides>
19/10Kajiwara-Payne tropicalization II (Trevor Gunn)
26/10Giansiracusa tropicalization (Stefano Mereta) <slides>
02/11Ordered blue schemes I (Manoel Jarra) <slides>
09/11Ordered blue schemes II (Manoel Jarra) <slides> /
Tropicalization as a base change I (Hernán Iriarte) <slides>
16/11Tropicalization as a base change II (Hernán Iriarte) <slides>
23/11Tropical ideals (Diane Maclagan)
30/11Algebraic K-theory and Grothendieck-Witt theory of monoid schemes (Matthew B. Young) <slides>
07/12Toric Hall algebras (Matthew Szczesny)
14/12Problem session

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