The analogue of Hilbert’s 10th problem over the rational numbers is wide open. It asks whether or not there is an algorithm for checking the solubility of a given homogenous Diophantine equation over the integers. What about if you are allowed to pick a Diophantine equation at random? Assuming that the number of variables exceeds the degree it has been conjectured by Poonen and Voloch that 100% of these equations satisfy the local-global principle, which in turn gives an algorithm for checking solubility. I shall report on recent work with Pierre Le Boudec and Will Sawin that comes close to this conjecture by using techniques from the geometry of numbers.
Random Diophantine equations
22.10.2019 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: