Wednesday, December 06, 2017 at 4:15pm to 5:15pm
SPEAKER: Brandon Hanson (Penn State)
TITLE: Additive quadratic correlation and the inverse problem for the large sieve
Sieves are tools to understand sequences which are forbidden from intersecting certain arithmetic progressions. When the number of forbidden progressions is very large, the Large Sieve, a fundamental tool in analytic number theory, allows us to get very strong information. The Large Sieve estimate is also sharp, but all known examples of sets which are extremal for the Large Sieve have the same structure - they look like quadratic sequences. That this is always the case is the "Inverse Large Sieve Conjecture". I will survey some known results about this conjecture and discuss the proof of a new theorem which gives evidence toward the conjecture of an additive combinatorics flavour. I hope to make the talk totally elementary and accessible.