BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jozsef Solymosi\, Kyle Chi Hoi Yip and Ethan White (University of British Columbia) DTSTART:20210805T171500Z DTEND:20210805T184500Z DTSTAMP:20260416T224413Z UID:CCM2021/5 DESCRIPTION:Title: Lacunary polynomials over finite fields and their applications\nby Joz sef Solymosi\, Kyle Chi Hoi Yip and Ethan White (University of British Col umbia) as part of Carleton Combinatorics Meeting 2021\n\n\nAbstract\nIn th e early 70's Laszlo Redei published a book titled "Lacunary Polynomials Ov er Finite Fields". In Redei's notation a polynomial $f(x)$ is lacunary if there is a gap between its largest and second largest exponent. For exampl e $x^5-2x+1$ is a lacunary polynomial. His book is about the properties an d applications of lacunary polynomials. His most important application is bounding the number of directions determined by point sets in an affine G alois plane. We revisit his work giving better bounds on the number of dir ections determined by a Cartesian product. As an immediate corollary we gi ve an upper bound on the clique number of a Paley graph. After the intro ( by Jozsef Solymosi) Kyle Yip will talk about the Van Lint-MacWilliams' con jecture and maximum cliques in Cayley graphs over finite fields and then E than White will talk about the number of distinct roots of a lacunary poly nomial over finite fields.\n LOCATION:https://researchseminars.org/talk/CCM2021/5/ END:VEVENT END:VCALENDAR