Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Vladimir Mitankin
Affiliation:

Universidade Federal do Rio de Janeiro/MPIM
Date:

Wed, 2019-01-30 14:30 - 15:30 In 2017 Ghosh and Sarnak conjectured how often the integral Hasse

principle should fail in a family of Markoff surfaces with evidence based

on numerical experiments. Using reduction theory they were able to obtain a

lower bound which is of magnitude still far away from the expected size. In

this talk we shall explain what can be achieved with techniques from

Arithmetic geometry. In particular, we get sharp bounds for the number of

failures of the integral Hasse principle explained by the Brauer-Manin

obstruction and a lower bound for the number of failures which are not

explained by the Brauer-Manin obstruction. This talk is based on a join

work with Dan Loughran.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/246