Spectral sets, tiling and sumsets
This talk is not only about mathematics. It is about me and mathematics. I will take the opportunity to review some of my results of recent years. In particular, I will briefly discuss the solution of the Fuglede conjecture concerning tiles and spectral sets in R^n, and explain accordingly how my research interest shifted towards sumsets and other problems of additive combinatorics. I will then mention some more recent results about the superadditive and submultiplicative nature of cardinalities of sumsets, and a general version of Plunnecke's inequality. Additive combinatorics is one of the most active fields of mathematics today with contributions from several world class researchers and with surprising applications to many other fields.
Some of the results in this talk are joint with M. Kolountzakis, while others with K. Gyarmati and I. Ruzsa.