Counting failures of a local-global principle
Date
Thursday, November 28, 2019 14:00 - 16:00
Speaker
Rachel Newton (University of Reading, UK)
Location
Heinzel Seminar Room / Office Bldg West (I21.EG.101)
Series
Seminar/Talk
Tags
Mathematics and CS Seminar
Host
Timothy Browning
Contact
Methods for solving polynomial equations in the integers and rationals have been sought and studied for thousands of years. Modern approaches try to piece together 'local' (meaning real and p-adic) information to decide whether a polynomial equation has a 'global' (meaning rational) solution. I will describe this approach and its limitations, with the aim of quantifying how often the local-global method fails within families of polynomial equations arising from the norm map between fields, as seen in Galois theory. I will present results from two joint papers: one with Tim Browning and the other with Christopher Frei and Daniel Loughran