Pure Maths Colloquium: Misha Rudnev
This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at https://theran.lt/pure-colloquium/.
| Where: | MI Theatre C |
| When: | Mar 30 2023 @ 16.00 | Video: | Not recorded |
| Speaker: | Misha Rudnev University of Bristol |
| Title: | On the sum-product conjecture, in particular sums and products of integers with few prime factors |
The talk will describe the state of the art of the Erdös-Szemerédi sum-product conjecture, a central open question in arithmetic combinatorics. It will also sketch the proof of a new result showing that for a set \(A\) of \(N\) integers, each of which has a small number of prime factors (roughly, at most \(log log N\) of them), either the product set \(AA\) is big or there is a large subset, with small additive energy (alias the number of additive quadruples, or the second moment of the convolution of \(A\) with itself).
Quantitatively, what stands for big and small is optimal, up to sub-polynomial factors of \(N\).