In the middle of the sixties, A. Lichnerowicz raised the following simple question: “Is the round sphere the only compact Riemannian manifold admitting a noncompact group of conformal transformations?” The talk will present the developments which arose from Lichnerowicz's question. It will be an opportunity to see diverse aspects of conformal dynamics in Riemannian, as well as Lorentzian geometry
This is the first of two talks in which the speaker will discuss the development of the theory of Toeplitz matrices and determinants in response to questions arising in the analysis of the Ising model of statistical mechanics. The first talk will be largely historical and the second will describe the state of the art today, including recent results of the speaker and his colleagues Alexander Its and Igor Krasovsky.
This talk is designed for a general mathematical audience; no prior knowledge of type theory is presumed.