12 марта в 18:30 (МСК) на Большом семинаре CombGeoLab выступит Dmitrii Zakharov.

Название доклада: Sets with moderate doubling

Аннотация:
Let A be a subset in an abelian group G such that |A+A| < |A|^{1.99}. In this case we say that A has moderate doubling. What can be said about the structure of A? Essentially nothing is known about this problem. If instead 1.99 we put 1.01, i.e. consider sets A with small doubling, then the Polynomial Freiman-Ruzsa conjecture predicts that A has to be close to to a subgroup (or Bohr set).
We discuss examples and possible conjectures about the structure of moderate doubling sets. We prove that in the case of G = F_2^n, the set A must intersect significantly with a subgroup coset. We follow the entropic approach which was used in the recent resolution of the PFR conjecture over F_2.

Joint work with Alex Cohen.

Ссылка на доклад:
https://us02web.zoom.us/j/82214467974?pwd=9bbtIr8GMwIQ6cQmgacqdeDhL6IAhn.1