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SUMMARY:Sumsets of sets of positive density in the integers
DTSTART:20260703T121500Z
DTEND:20260703T134500Z
DTSTAMP:20260702T051600Z
UID:indico-event-1434@math-events.uni-bonn.de
DESCRIPTION:Speakers: Ethan Ackelsberg (EPFL)\n\nAbstract: \nA central ob
 ject of study in additive combinatorics is the sumset $A+B$ of two sets $A
 $ and $B$. Two of the basic questions one may ask are direct questions ("h
 ow large must $A+B$ be in terms of the sizes of $A$ and $B$?") and inverse
  questions ("if $A+B$ is small\, what can be deduced about the structure o
 f $A$ and $B$?"). When $A$ and $B$ are infinite subsets of the integers wi
 th size quantified by natural density $d(·)$\, Kneser (1953) proved the d
 irect theorem that $d(A+B) \\ge d(A) + d(B)$ unless $A$ and $B$ have certa
 in modular obstructions. Erdős and Graham (1980) asked for a correspondin
 g inverse theorem classifying sets with $d(A+B) = d(A) + d(B)$. In this ta
 lk\, we will present a new result characterizing the pairs of sets satisfy
 ing $d(A+B) = d(A) + d(B)$ in the absence of modular obstructions. We will
  also highlight some of the key Fourier analytic and ergodic theoretic asp
 ects of the proof. This talk is based on joint work with Florian K. Richte
 r. \n \n\nhttps://math-events.uni-bonn.de/event/1434/
LOCATION:Endenicher Allee 60\, Seminarraum 0.011 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/1434/
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