BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Haydar Göral (İYTE) DTSTART:20240322T124000Z DTEND:20240322T134000Z DTSTAMP:20260423T052712Z UID:OBAGS/43 DESCRIPTION:Title: A rithmetic Progressions in Finite Fields\nby Haydar Göral (İYTE) as p art of ODTU-Bilkent Algebraic Geometry Seminars\n\n\nAbstract\nIn 1927\, v an der Waerden proved a theorem regarding the existence of arithmetic prog ressions in any partition of the positive integers with finitely many clas ses. In 1936\, a strengthening of van der Waerden's theorem was conjecture d by Erdös and Turan\, which states that any subset of positive integers with a positive upper density contains arbitrarily long arithmetic progres sions. In 1975\, Szemeredi developed his combinatorial method to resolve t his conjecture\, and the affirmative answer to Erdös and Turan's conjectu re is now known as Szemeredi's theorem. As well as in the integers\, Szeme redi-type problems have been extensively studied in subsets of finite fiel ds. While much work has been done on the problem of whether subsets of fin ite fields contain arithmetic progressions\, in this talk we concentrate o n how many arithmetic progressions we have in certain subsets of finite fi elds. The technique is based on certain types of Weil estimates. We 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 best possi ble when k is small\, owing to the Sato-Tate conjecture. This work is supp orted by the Scientific and Technological Research Council of Turkey with the project number 122F027.\n LOCATION:https://researchseminars.org/talk/OBAGS/43/ END:VEVENT END:VCALENDAR