Title: Positive definite functions and mutually unbiased bases 

Abstract: I will present a new approach to the problem of mutually unbiased bases (MUBs), based on positive definite functions on the unitary group. The method provides a new proof of the fact that there are at most d+1 MUBs in complex dimension d, and it may also lead to a proof of non-existence of complete systems of MUBs in dimension 6 via a conjectured algebraic identity. Joint work with Mihalis Kolountsakis and Mihaly Weiner.