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Avoiding arithmetic progressions or right angles

In this talk we discuss some bounds about sets avoiding certain arithmetic or geometric configurations in F_p^n (or more generally, in Z_m^n). In particular, we will consider the case of 6-term arithmetic progressions in Z_6^n, and sets avoiding right angles in F_p^n. Our methods can also be used to bound the maximum possible size of a binary code where no two codewords have Hamming distance divisible by a fixed prime p. Joint work with Palincza and with Bursics, Matolcsi and Schrettner.