Mini-Workshop on Cremona groups and Grothendieck rings
Are Cremona groups generated by involutions ?
Generating the plane Cremona group by involutions
Julia Schneider
The plane Cremona group over a field k is the group of birational transformations of the plane that are defined over k. In this talk I consider the case when k is a perfect field (e.g. any field in characteristic zero, finite fields, etc) and I will discuss the following theorem: The plane Cremona group over any perfect field is generated by involutions. A direct corollary of this result is that all (non-trivial) elements in the abelianisation of the plane Cremona group have order two. This is joint work with Stéphane Lamy.
The plane Cremona group and Grothendieck rings
Susanna Zimmermann
A birational map of the plane over some perfect field that has a base-point of degree d needs to contract a curve with d irreducible components. This is intuitive, but actually not straight forward unless the field is particular. I'll explain how to prove the statement by using L-equivalence of curves.
Motivic invariants of birational maps
Evgeny Shinder
I will introduce variants of the Grothendieck group of varieties, and explain some invariants of birational maps taking values in these groups. I will explain geometric constructions of birational maps with nonvanishing motivic invariants, state some open problems, and give applications to Cremona groups. This is joint work with Hsueh-Yung Lin.
Practical
Participants
(*= virtual participation)
- Ignacio Barros Reyes (LMO)
- Frank Benoist (LMO)
- Pietro Beri (Université de Poitiers)
- Marcello Bernardara (Université Toulouse 3)
- Fabio Bernasconi (EPFL)
- Cinzia Bisi* (University of Ferrara)
- Jérémy Blanc (Université de Bâle)
- Aurore Boitrel (Université d'Angers)
- Jean-Baptiste Campesato (Université d'Angers)
- Mani Esna Ashari (Université de Bâle)
- Andrea Fanelli (Institut de Mathématiques de Bordeaux)
- Pascal Fong (Université de Bâle)
- Liana Heuberger (Université d'Angers)
- Alexandra Kuznetsova (École Polytechnique)
- Kuan-Wen Lai (University of Bonn)
- Stéphane Lamy (Université Toulouse 3)
- Clementine Lemarie-Rieusset (Université de Dijon)
- Hsueh-Yung Lin* (Université Nationale de Taïwan)
- Anne Lonjou (LMO)
- Emanuele Macrì (LMO)
- Mario Morán Cañón* (University of Oklahoma)
- Anne Moreau (LMO)
- Fabrice Orgogozo (IMJ-PRG)
- Dmitrii Pirozhkov (Université de Paris)
- Angel Rios (Universita di Roma)
- Julia Schneider (Université Toulouse 3)
- Julien Sebag* (Université Rennes 1)
- Evgeny Shinder (University of Sheffield)
- Benjamin Sung (Northeastern University)
- Christian Urech (EPFL)
- Egor Yasinksy (École Polytechnique)
- Mikhail Zaidenberg* (Université Grenoble Alpes)
- Sokratis Zikas (Université de Bâle)
- Susanna Zimmermann (Université d'Angers)
Organizers
Sponsors
