The second moment of the size of the 2Selmer group of elliptic curves
The second moment of the size of the 2Selmer group of elliptic curves

Ashvin Swaminathan, Princeton University
Fine Hall 214
InPerson and Online Talk
Zoom link: https://princeton.zoom.us/j/97126136441
Passcode: The three digit integer that is the cube of the sum of its digits
We introduce a new orbit parametrization for square roots of the class of the inverse different in rings cut out by binary forms. This parametrization has many applications of interest in arithmetic statistics; for example, we use it to prove that the second moment of the size of the 2Selmer group of elliptic curves is at most 15, confirming a conjecture of Poonen and Rains.