The Sharp Threshold for Making Squares

Explore a 46-minute conference talk by Rob Morris from IMPA, presented at the Alan Turing Institute as part of the large-scale structures in random graphs workshop. Delve into the problem of determining the threshold for finding subsequences with square products in random integer sequences, a crucial aspect of factoring large integers. Learn about Pomerance's 1994 ICM problem, subsequent bounds, and the recent breakthrough by Croot, Granville, Pemantle, and Tetali. Discover the proof of their conjecture, combining number theory and probabilistic combinatorics techniques, including a self-correcting random process of non-uniform hypergraphs. Gain insights into this collaborative work with Paul Balister and Béla Bollobás, supported by the Heilbronn Institute for Mathematical Research, The Alan Turing Institute, and the LSE Department of Mathematics.

The sharp threshold for making squares, Rob Morris (IMPA)