SEMINARIO DE ÁLGEBRA Y COMBINATORIA

**SEMINARIO DE ÁLGEBRA Y COMBINATORIA**

**Anne de Roton**

**(Nancy)**

*"Small sumsets in $mathbb{R}$"*

**Miercoles 23 de noviembre a las 11:30. Módulo 17, Aula 520**

** Abstract: **

**Freiman's inverse theorems are central results in additive combinatorics that characterize finite subsets $A$ and $B$ of a discrete abelian group such that the sumset $A+B$ is rather small. In this talk, we shall explain how to get a full continuous version of Freiman's so-called ``$3k-4$ theorem" for small sumsets in $mathbb{R}$, by using some ideas from Ruzsa's work on measures of sumsets in $mathbb{R}$ as well as some graphic representation of density functions of sets. We thereby get some structural properties of $A$, $B$ and $A+B$ when $lambda(A+B)**lambda(B)$ and either $lambda(A)geqlambda(B)$ or $A$ has larger diameter than $B$. We also give some structural information on sets of large density according to the size of their sumset, a result so far unknown in the discrete and the continuous setting.

Location Miercoles 23 de noviembre a las 11:30. Módulo 17, Aula 520