Palestra: On the singularity of random symmetric matrices
Palestrante: Letícia Mattos (IMPA)

Data: 13 de maio de 2019 (segunda-feira)
Hora: 15:30
Local: B106-a – Bloco B - CT – Instituto de Matemática - UFRJ

Resumo: A well-known conjecture states that a random symmetric n-by-n matrix with entries in {-1,1} is singular with probability 2^{-n+o(1)}. In this talk we will show that the probability of this event is at most 2^{-cn^(1/2)}, improving the best known bound 2^{-cn^(1/4)}, which was obtained recently by Ferber and Jain. The main new ingredient is an inverse Littlewood--Offord theorem in Z_p^n that applies under very mild conditions, whose statement is inspired by the method of hypergraph containers. This is a joint work with Marcelo Campos, Robert Morris and Natasha Morrison.