Boris Solomyak (BIU): On the Pisot substitution conjecture

Tue, 07/12/202112:00-13:00

Abstract. The conjecture states that a substitution whose incidence matrix is "Pisot", that is, all of its eigenvalues, except the dominant, Perron-Frobenius eigenvalue,
lie inside the unit circle, gives rise to a measure preserving system with pure discrete spectrum. It is still open, although many special cases are known. I will survey the history and discuss some methods used to attack the problem.