This is joint work with Dan Loughran. A theorem of Serre states that almost all plane conics over Q have no rational point. We prove a version of this result for families of conics parametrized by elliptic curves using elliptic divisibility sequences and a version of the Selberg sieve for elliptic curves. We also give more general results for specializations of Brauer groups, which yields applications to norm form equations.
This year our seminar is running with a new format to try to promote more interaction in our Zoom world. The idea is to have a shorter talk with regular 5min Q&A breaks sprinkled throughout. The exact schedule will be left up to the speaker, but an example of what we're envisioning is as follows: