# An enhancement of the Inter-universal Teichmüller theory and a range of applications (Ivan Fesenko, University of Nottingham)

26.09.2019 16:15

It is a typical phenomenon in number theory that the residue characteristic 2 requires special considerations in comparison to odd residue characteristic. Quadratic reciprocity law and the IUT theory of Shinichi Mochizuki are some of such situations. I will talk about a recent paper of 5 coauthors: Sh. Mochizuki, W. Porowski, A. Minamide, Yu. Hoshi and I, which allowed to incorporate even residue characteristic in an (slightly) enhanced IUT theory. This leads to the first proof of several versions of effective abc inequality. It then leads to further applications to FLT (independently of Wiles and Taylor) and other Diophantine equations. Two interesting aspects are the astronomical scale of explicit constants and the restoration in number theory of the importance of various work of many people on FLT produced before the Wiles-Taylor work.

PS. The Colloquium will be followed by an aperitif

### Lieu

Room 17

### Organisé par

Section de mathématiques### Intervenants

Ivan Fesenko, University of Nottinghamentrée libre

### Classement

Catégorie: Colloque