16:00
On Unique Sums in Abelian Groups
Abstract
In this talk, we will study the problem in additive combinatorics of determining for a finite Abelian group $G$ the size of its smallest subset $A\subset G$ that has no unique sum, meaning that for every two $a_1,a_2\in A$ we can write $a_1+a_2=a’_1+a’_2$ for different $a’_1,a’_2\in A$. We begin by using classical rectification methods to obtain the previous best lower bounds of the form $|A|\gg \log p(G)$, which stood for 50 years. Our main aim is to outline the proof of a recent improvement and discuss some of its key notions such as additive dimension and the density increment method. This talk is based on Bedert, B. On Unique Sums in Abelian Groups. Combinatorica (2023).
Professor Matthew Botvinick (Director of Neuroscience Research, DeepMind) - AI and the Challenge of Human Co-operation
Thursday 16th May, 5 pm, Mathematical Institute Lecture Theatres 1 and 2. The Lecture will also be livestreamed.
Admission is free, but booking is required.