Dynamical Systems and Analysis Seminar - Ethan Ackelsberg
| Dates: | 18 May 2026 |
|---|
| Times: | 14:00 - 15:00 |
|---|
| What is it: | Seminar |
|---|
| Organiser: | Department of Mathematics |
|---|
| Who is it for: | University staff, External researchers, Current University students |
|---|
|
Speaker: Ethan Ackelsberg (EPFL)
Title: Sumsets of sets of positive density in the integers
Abstract: A central object 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 (“how 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 of A and B?”). When A and B are infinite subsets of the integers with size quantified by natural density d(·), Kneser (1953) proved the direct theorem that d(A+B) ? d(A) + d(B) unless A and B have certain modular obstructions. Erd?s and Graham (1980) asked for a corresponding inverse theorem classifying sets with d(A+B) = d(A) + d(B). In this talk, we will discuss some history of direct and inverse theorems in additive combinatorics and present a new result characterizing the pairs of sets satisfying d(A+B) = d(A) + d(B) in the absence of modular obstructions. In the course of the talk, we will see how ideas from analysis and ergodic theory come into play.
Room: Frank Adams 1
Further information: https://personalpages.manchester.ac.uk/staff/yotam.smilansky/dynamics_analysis
Travel and Contact Information
Find event
Frank Adams 1
Alan Turing Building
Manchester
