Discrete Math seminar continues this week with Swaroop Hegde from the University of Georgia. Swaroop will be joining us on zoom to tell us about an inverse result for Ruzsa’s inequality on triple sumsets (abstract below). We will have a watch party in Carver 401, 2:10-3pm on Thursday as usual, and you are also welcome to join over zoom [link].
https://iastate.zoom.us/j/99922097329?pwd=SVlMSmU0dXBlMFY3YlNlVjBQOVpuZz09
Abstract: Ruzsa’s inequality on triple sumsets states that if A is a finite subset of a commutative group then |A+A+A| is at most |A+A|^{3/2}. Ruzsa has constructed a family of examples which show that this inequality is sharp asymptotically, upto a constant factor. In this talk, I will present a new proof of this inequality which improves the constant in the upper bound to (\sqrt{2}/3 + o(1)). This proof shows a connection to Kruskal-Katona type results while also allowing us to obtain a stability version of Ruzsa’s inequality which describes near optimal structures. I will then present an inverse result which gives structural information about A even if |A+A+A| is much farther from the upper bound than required in the stability result.