Analysis Seminar

This talk begins with an introduction to noncommutative (nc) Taylor remainders for functions taking values in algebras of bounded operators. I will then present a fundamental trace formula expressing the trace of these remainders in terms of the spectral shift function (SSF), with particular attention to the question of its sign-definiteness. In the second part of the talk, I will discuss the BMV conjecture in both finite- and infinite-dimensional settings.