Recorded 10 February 2022. Joe Neeman of the University of Texas at Austin presents "Large deviations for triangle densities" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: Borell's inequality characterizes the boolean-valued functions on Gaussian space that have extremal Gaussian noise stability. We prove a similar inequality for functions that take values in the sphere. We will also briefly discuss an application to the computational complexity of approximating certain quantum ground states.