Masahiro Nakahara, University of Washington

Zoom (UW Math department members can access the zoom link at https://sites.math.washington.edu/intranet/WholeDept/zoom.php )
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:
710 minutes of Introduction/Motivation/Background
5 min Q&A, e.g. asking for further examples, more details on what is already known, or clarifying questions
710 minutes of Statement of results/Prior work or ideas of proof
5 min Q&A, e.g., asking about hypotheses, connecting statements to previous work mentioned in the first slot, etc.
1520 minutes of discussion of the proof: could be entirely speakerled, or could be more of back and forth with the audience, depending on the topic.