BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lillian Pierce (Duke University) DTSTART:20201215T213000Z DTEND:20201215T223000Z DTSTAMP:20260423T130355Z UID:MITNT/18 DESCRIPTION:Title: O n superorthogonality\nby Lillian Pierce (Duke University) as part of M IT number theory seminar\n\n\nAbstract\nThe Burgess bound is a well-known upper bound for short multiplicative character sums\, which implies for ex ample a subconvexity bound for Dirichlet L-functions. Since the 1950's\, p eople have tried to improve the Burgess method. In order to try to improve a method\, it makes sense to understand the bigger “proofscape” in wh ich a method fits. The Burgess method didn’t seem to fit well into a big ger proofscape. In this talk we will show that in fact it can be regarded as an application of “superorthogonality.” This perspective links topi cs from harmonic analysis and number theory\, such as Khintchine’s inequ ality\, Walsh-Paley series\, square function estimates and decoupling\, mu lti-correlation sums of trace functions\, and the Burgess method. We will survey these connections in an accessible way\, with a focus on the number theoretic side.\n LOCATION:https://researchseminars.org/talk/MITNT/18/ END:VEVENT END:VCALENDAR