Manchester Number Theory Seminar - Ross Paterson
| Dates: | 19 November 2024 |
|---|
| Times: | 15:00 - 16:00 |
|---|
| What is it: | Seminar |
|---|
| Organiser: | Department of Mathematics |
|---|
| Who is it for: | University staff, External researchers, Current University students |
|---|
|
Speaker: Ross Paterson (University of Bristol)
Title: Quadratic Twists as Random Variables
Abstract: This talk will be concerned with the statistical behaviour of Selmer groups. We will begin by motivating the study of Selmer groups generally, describing the general picture around them and how they reveal information about objects of interest to us, for example class groups of number fields and Mordell--Weil groups of elliptic curves. We will then focus on a particular case of interest: 2-Selmer groups of elliptic curves. Specifically, if we fix a quadratic field K then for every elliptic curve E/Q there is an associated twist of E by K which is another elliptic curve E_d/Q. The 2-Selmer groups of E and of E_d naturally lie in the same space, and we are motivated to study their independence as E varies. We shall present a heuristic in this direction, and some results in support of it. We will conclude by explaining what this tells us about the behaviour of the group of points on E over K.
Room: Frank Adams 1
Travel and Contact Information
Find event
Frank Adams 1
Alan Turing Building
Manchester
