In this talk, we explore orthonormal Strichartz estimates associated with a general self-adjoint operator $L$ on $L^2(X,\mu)$, under some assumption on the kernel of the Schr"{o}dinger propagator $e^{itL}$, where $(X,\mu)$ is a measure space. As an application of these orthonormal Strichartz estimates, we will discuss the well-posedness of the Hartree equation within the framework of Schatten spaces. Additionally, we extend the discussion to orthonormal smoothing estimates, which extend prior work of Kenig-Ponce-Vega for single functions.

The video of this talk is available on the IISc Math Department channel.