BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hunter Spink (Stanford University) DTSTART:20210715T141500Z DTEND:20210715T160000Z DTSTAMP:20260422T070021Z UID:CJCS/24 DESCRIPTION:Title: Ge ometric and o-minimal Littlewood-Offord problems\nby Hunter Spink (Sta nford University) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\ n\nAbstract\n(Joint with Jacob Fox and Matthew Kwan\, no o-minimal backgro und required!) The classical Erdős-Littlewood-Offord theorem says that fo r any n nonzero vectors in $\\mathbb{R}^d$\, a random signed sum concentra tes on any point with probability at most $O(n^{-1/2})$. Combining tools f rom probability theory\, additive combinatorics\, and o-minimality\, we ob tain an anti-concentration probability of $n^{-1/2+o(1)}$ for any o-minima l set $S$ in $\\mathbb{R}^d$ (such as a hypersurface defined by a polynomi al in $x_1\,...\,x_n\,e^{x_1}\,...\,e^{x_n}$\, or a restricted analytic fu nction) not containing a line segment. We do this by showing such o-minima l sets have no higher-order additive structure\, complementing work by Pil a on lower-order additive structure developed to count rational and algebr aic points of bounded height.\n LOCATION:https://researchseminars.org/talk/CJCS/24/ END:VEVENT END:VCALENDAR