Department of

January 2020 February 2020 March 2020 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 1 1 2 3 4 5 6 7 5 6 7 8 9 10 11 2 3 4 5 6 7 8 8 9 10 11 12 13 14 12 13 14 15 16 17 18 9 10 11 12 13 14 15 15 16 17 18 19 20 21 19 20 21 22 23 24 25 16 17 18 19 20 21 22 22 23 24 25 26 27 28 26 27 28 29 30 31 23 24 25 26 27 28 29 29 30 31

Thursday, February 13, 2020

**Abstract:** We describe a probabilistic model that describes the statistical behavior of the divisors of integers, divisors of permutations and divisors of polynomials over a finite field. We will discuss how this can be used to obtain new bounds on the concentration of divisors of integers, improving a result of Maier and Tenenbaum. This is joint work with Ben Green and Dimitris Koukoulopoulos.