Data: 18/06/2020, às 14:00 horas (GMT-3, horário de Brasília).
Título: Asymmetric containers and additive combinatorics
Palestrante: Rob Morris (IMPA)
The method of hypergraph containers has found a large number of applications in probabilistic combinatorics since its introduction in 2015. However, it does not seem possible to apply the usual container lemma to counting problems that involve sumsets. Recently, however, Campos discovered that (surprisingly) an asymmetric variant of the container lemma, introduced recently by Morris, Samotij and Saxton, can be applied to such problems.
In this talk I will describe Campos' original application, which resolved a conjecture of Alon, Balogh, Morris and Samotij, and a further application, which determines very precisely the typical structure of sets with small sumset. I will also mention some related work on random matrices. The talk will be non-technical, and no previous knowledge of containers, sumsets, or random matrices will be assumed.
This talk is based on joint work with Marcelo Campos, Maurício Collares, Letícia Mattos, Natasha Morrison, Wojciech Samotij, David Saxton, and Victor Souza.