Christian Elsholtz (Graz): Arithmetic progressions in arithmetic sets

Austrian-Hungarian Diophantine Number Theory seminar
https://uni-salzburg.webex.com/uni-salzburg/j.php?MTID=m119b11618f0fcbf1c2f72bdc42ca0e55

Abstract: We study the length of arithmetic progressions in arithmetically interesting sets. For the set of squares this question goes back to Fermat (there are no 4 squares in progression). We discuss new upper bounds in the value set of binary quadratic forms and norm forms (joint work with C. Frei), discuss long gaps between sums of two squares (joint with R. Dietmann, A. B. Kalmynin, S. Konyagin, and J. Maynard), and make a new observation on long progressions in sums of S-units.