Hello, my name is Ralph Xu. I am a PhD student at Syracuse University.

I study Riemannian geometry, with a focus on curvature in weighted settings. My recent work centers on weighted sectional curvature, N-Bakry-Émery Ricci curvature, and the newly introduced notion of weighted intermediate Ricci curvature, which interpolates between the two. These weighted curvatures naturally arise in the study of metric measure spaces, Ricci flow, and diffusion processes, and they provide a flexible framework for extending classical geometric results beyond the unweighted setting.

Beyond these results, I am interested in exploring how weighted curvature conditions interact with simplicial volume, the Thurston norm, and (pseudo) Anosov flows, with the goal of developing new techniques that connect Riemannian geometry to problems in low dimensional topology, dynamical systems, and mathematical physics.

My advisor is William Wylie.

I am on the job market this year!