Marc Technau: Cilleruelo's conjecture on the LCM of polynomial sequences

Abstract.

We discuss a conjecture of Cilleruelo on the growth of the least common multiple of consecutive values of a polynomial and subsequent progress towards it in work of Rudnick–Maynard and Sah. In recent work, the speaker and, independently, Alexei Entin made further advances by exploiting symmetries amongst the roots of the polynomials in question. We shall discuss these approaches and related beautiful work of Baier and Dey.