# Meeting Details

Title: Sharp Gagliardo--Nirenberg--Sobolev inequalities and conformal geometry Department of Mathematics Colloquium Jeffrey Case, Princeton University There is a deep connection between curvature prescription problems in conformal geometry and sharp Sobolev inequalities. One famous example is the connection between prescribing conformal metrics with constant scalar curvature and the sharp $L^2$ Sobolev inequalty. Another example is the connection between prescribing Perelman's weighted scalar curvature and the sharp logarithmic Sobolev inequality. In this talk, I will describe an interpolating family of curvature prescription problems on smooth metric measure spaces which connect the scalar curvature to Perelman's weighted scalar curvature and are related to the family of sharp Gagliardo-Nirenberg-Sobolev inequalities discovered by Del Pino and Dolbeault. In particular, this provides a new perspective on Perelman's $W$-functional and suggests an approach to finding higher order analogues.