BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Oliver Roche-Newton (Johann Radon Institute for Computational and Applied Mathematics (RICAM)\, Austria) DTSTART:20200604T140000Z DTEND:20200604T142500Z DTSTAMP:20260423T011238Z UID:CANT2020/45 DESCRIPTION:Title: Higher convexity and iterated sum sets\nby Oliver Roche-Newton (Joha nn Radon Institute for Computational and Applied Mathematics (RICAM)\, Aus tria) as part of Combinatorial and additive number theory (CANT 2021)\n\n\ nAbstract\nAn important generalisation of the sum-product phenomenon is th e basic idea \nthat convex functions destroy additive structure. This idea has perhaps been most notably \nquantified in the work of Elekes\, Nathan son and Ruzsa\, in which they used incidence geometry \nto prove that at l east one of the sets $A+A$ or $f(A)+f(A)$ must be large.\n\nI will discuss joint work with Hanson and Rudnev\, in which we use a stronger notion of convexity \n to make further progress. In particular\, we show that\, if $ A+A$ is sufficiently small and $f$ \nsatisfies this hyperconvexity conditi on\, then we have unbounded growth for sums of $f(A)$. \nThis in turn give s new results for iterated product sets of a set with small sum set.\n\nTi tle: An update on the state-of-the-art sum-product inequality over the rea ls \nAbstract: The aim of this somewhat technical talk is to clarify the u nderlying constructions \nand present a streamlined step-by-step self-cont ained proof of the sum-product inequality \nof Solymosi\, Konyagin and Shk redov. The proof ends up with a slightly better exponent \n$4/3+2/1167$ th an the previous world record. \n\nJoint work with Sophie Stevens.\n LOCATION:https://researchseminars.org/talk/CANT2020/45/ END:VEVENT END:VCALENDAR