Nonnegative Ricci curvature and virtual abelianness in dimensions less than 12
Jiayin Pan (潘佳垠)
I am an Assistant Professor at Department of Mathematics, University of California, Santa Cruz.
I work in Riemannian geometry; more precisely, the interplay between Ricci curvature and topology, (equivariant) Gromov-Hausdorff convergence, and Ricci limit spaces. I am also interested in sectional curvature, Lorentzian geometry, and subRiemannian geometry.
I received my Ph.D. degree in 2018 from Rutgers University - New Brunswick, advised by Xiaochun Rong. Before coming to UC Santa Cruz, I was a Visiting Assistant Professor at UC Santa Barbara during AY 18-21, and a Fields Postdoctoral Fellow at Fields Institute during AY 21-22.
Email address: jpan53 at ucsc dot edu or jypan10 at gmail dot com
Office: McHenry 4178
Office hours: (F26) TBD
Pronouns: he/they
Besides mathematics, I enjoy reading election analysis, playing Metroidvania and puzzle games, and hiking.
Research Articles
The articles are listed in the reverse order they were finished and submitted to arXiv. The preprints can be found on arXiv (link).
Complete manifolds with nonnegative Ricci curvature and slow relative volume growth
Universal non-CD of sub-Riemannian manifolds
On the topology of manifolds with nonnegative Ricci curvature and linear volume growth
Nonnegative Ricci curvature, splitting at infinity, and first Betti number rigidity
Ricci curvature and fundamental groups of effective regular sets
Nonnegative Ricci curvature, nilpotency, and Hausdorff dimension
The Grushin hemisphere as a Ricci limit space with curvature ≥1
Singular Weyl’s law with Ricci curvature bounded below
Examples of open manifolds with positive Ricci curvature and non-proper Busemann functions
Nonnegative Ricci curvature, metric cones, and virtual abelianness
Examples of Ricci limit spaces with non-integer Hausdorff dimension
Some topological results of Ricci limit spaces
Nonnegative Ricci curvature and escape rate gap
On the escape rate of geodesic loops in an open manifold with nonnegative Ricci curvature
Semi-local simple connectedness of noncollapsing Ricci limit spaces
Nonnegative Ricci curvature, almost stability at infinity, and structure of fundamental groups
Ricci curvature and isometric actions with scaling nonvanishing property
Nonnegative Ricci curvature, stability at infinity, and finite generation of fundamental groups
A Proof of Milnor conjecture in dimension 3
Survey Articles
The fundamental groups of open manifolds with nonnegative Ricci curvature
Universal covers of Ricci limit and RCD spaces
Some notes/slides
Nonnegative Ricci curvature, nilpotency, and asymptotic geometry Video slides
A talk that I gave at SLMath workshop “Recent progress on geometric analysis and Riemannian geometry”.
An Invitation to Gromov-Hausdorff convergence slides
An introductory talk on Gromov-Hausdorff convergence.
Nonnegative Ricci curvature and virtually abelian structure file
A short note about the fundamental groups of closed manifolds of zero sectional curvature or non-negative Ricci curvature.
Notes on Rong’s cyclicity theorem file
A beautiful theorem by Xiaochun Rong.
Derivatives and Curvature in a nutshell file
Supplemental notes for undergraduate course Classical Differential Geometry.
Non-Euclidean Geometry file
Lecture notes for undergraduate course Non-Euclidean geometry.
