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

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

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Ashvin Swaminathan, Princeton University
Fine Hall 214

In-Person 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 2-Selmer group of elliptic curves is at most 15, confirming a conjecture of Poonen and Rains.