Exploring the nature of approximate groups

Date:
21.11.2017

Speaker:
Michael Björklund

Time:
13:30 Uhr

An approximate group is a symmetric subset P of a given group G which is “almost” closed under multiplication in the sense that the product set P^2 is contained in a finite union of translates of P. Over the years, this weakened – and perhaps seemingly artificial – extension of the notion of a group has naturally (and independently) appeared in many different areas in mathematics.
I will begin the talk by surveying some of these appearences (ranging from the sumproduct phenomena of Erdos to Meyer’s quasicrystals), hopefully convincing you that these appearances are not forced.
During the last few years I have, in joint collaboration with Tobias Hartnick (Technion), spent a nontrivial amount of time to try to better understand approximate groups which are “large” and “discrete” in some ambient locally compact group G (we call these subsets approximate lattices). During the second half of the talk I will try to motivate this course of research and survey some of our findings.
No previous knowledge of approximate groups will be required.

Place:
1.067 (20.30)