Akshat Mudgal: Recent progress towards the sum–product conjecture and related problems (NTWS 197)
Channel: Number Theory Web Seminar
Date: 2024-02-02

Abstract: An important open problem in combinatorial number theory is the Erdös–Szemerédi sum–product conjecture, which suggests that for any positive integers s, N, and for any set A of N integers, either there are many s-fold sums of the form a_1 + … + a_s or there are many s-fold products of the form a_1…a_s. While this remains wide open, various generalisations of this problem have been considered more recently, including the question of finding large additive and multiplicative Sidon sets in arbitrary sets of integers as well as studying the so-called low energy decompositions.
In this talk, I will outline some recent progress towards the above questions, as well as highlight how these connect very naturally to other key conjectures in additive combinatorics.

Link to slides: https://drive.google.com/file/d/1BfhFTrdl9iP-m_PmH8PyFKVmmuE5kQUU

Number Theory Web Seminar: https://www.ntwebseminar.org

Original air date: 
Thursday, February 1, 2024 (8am PST, 11am EST, 4pm GMT, 5pm CET, 6pm Israel Standard Time, 9:30pm Indian Standard Time)
Friday, February 2, 2024 (12am CST, 3am AEDT, 5am NZDT)