BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Frederick Manners (University of California\, San Diego) DTSTART:20240130T213000Z DTEND:20240130T223000Z DTSTAMP:20260423T021035Z UID:MathPic/123 DESCRIPTION:Title: Inverse theorems and approximate structure\nby Frederick Manners (Un iversity of California\, San Diego) as part of Mathematical Picture Langua ge Seminar\n\nLecture held in Jefferson 256.\n\nAbstract\nWe call a functi on f linear if f(x+y) = f(x) + f(y) holds for all x\,y. It is natural to call f "99% linear" if instead\, this identity holds for most pairs (x\,y) \; say\, 99% of pairs. Similarly\, we could say f is "1% linear" if this identity holds 1% of the time. A natural question is then: what can we sa y about the structure of "99% linear" or "1% linear" functions? Are they always just perturbations of true 100% linear functions\, or are there oth er examples? Given almost any algebraic definition\, you can similarly ask about its approximate variants\, and if you can prove a strong positive s tatement\, it tends to have applications. In particular\, I will discuss how 1% linear functions relate to the Polynomial Freiman-Ruzsa conjecture\ , and how 1% polynomial functions relate to the Inverse Theorem for the Go wers norms.\n\nPasscode: 657361\n LOCATION:https://researchseminars.org/talk/MathPic/123/ END:VEVENT END:VCALENDAR