Since Lieb's celebrated work in 1973 resolving the conjecture of Wigner-Yanase-Dyson, the study of convexity/concavity of trace functionals has seen great progress. In this talk we will explain how to prove the convexity/concavity of a family of trace functionals without the information of ''second derivative''. Along the way we will revisit some historical results and settle a conjecture by Carlen-Frank-Lieb. A weaker form of this conjecture was made by Audenaert-Datta when studying the data processing inequalities in quantum information theory. We will discuss this as an application.

Zoom Meeting link: https://us02web.zoom.us/j/87669949245 Meeting ID: 876 6994 9245