Title：Atoms, Zero Divisors and Atiyah Conjecture
Speaker：Sheng Yin（University Paul Sabatier）
Time：16:00-17:00, November5
Location：Tecent Meeting, Tecent Meeting ID: 679 645 641
Abstract：Kaplansky’s zero divisor conjecture is a long-open conjecture which states that the group algebra CG is a domain if and only if the group G is torsion-free. This purely algebraic conjecture is deeply connected to an analytic (or topological) conjecture called the strong Atiyah conjecture. In this talk, we will present a connection of these problems to some problems on atoms of probability measures, which show up in free probability. Actually in free probability we are interested in more or less the same question (in some dis- guise) along the study of regularities of the probability distributions of non-commutative random variables.
This talk is based on the recent joint-work with Tobias Mai and Roland Speicher and an ongoing project with Octavio Arizmendi, Guillaume Cebron and Roland Speicher. We have proved that the absence of zero divisors for all rational functions in some non- commutative random variables. Along our investigation we discovery several rank equalities for the zero divisor problem in the context of free probability (or for Atiyah conjecture in the context of L2theory).
