BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Haydar Goral (Izmir Institute of Technology) DTSTART:20240221T140000Z DTEND:20240221T150000Z DTSTAMP:20260422T104735Z UID:FGC-IPM/47 DESCRIPTION:Title: Counting arithmetic progressions modulo p\nby Haydar Goral (Izmir Ins titute of Technology) as part of FGC-HRI-IPM Number Theory Webinars\n\n\nA bstract\nIn 1975\, Szemeredi gave an affirmative answer to Erdös and Tura n's conjecture which states that any subset of positive integers with a po sitive upper density contains arbitrarily long arithmetic progressions. Sz emeredi-type problems have also been extensively studied in subsets of fin ite fields. While much work has been done on the problem of whether subset s of finite fields contain arithmetic progressions\, in this talk we conce ntrate on how many arithmetic progressions we have in certain subsets of f inite fields. The technique is based on certain types of Weil estimates. W e obtain an asymptotic for the number of k-term arithmetic progressions in squares with a better error term. Moreover our error term is sharp and be st possible when k is small\, owing to the Sato-Tate conjecture. This work is supported by the Scientific and Technological Research Council of Turk ey with the project number 122F027.\n\npassword is 848084\n LOCATION:https://researchseminars.org/talk/FGC-IPM/47/ END:VEVENT END:VCALENDAR