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 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: (S23) By appointment
Pronouns: he/they

For AY 23-26, I am supported by National Science Foundation DMS-2304698 and Simons Foundation Travel Support for Mathematicians.

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.

(With Zhu Ye) 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
Updated Version (Added an Appendix to prove a claim used in the proof of Lemma 4.6)

The Grushin hemisphere as a Ricci limit space with curvature ≥1
Proc. Amer. Math. Soc. Ser. B. 10 (2023), 71-75, DOI

(With Xianzhe Dai, Shouhei Honda, and Guofang Wei) Singular Weyl’s law with Ricci curvature bounded below
Trans. Amer. Math. Soc. Ser. B, 10 (2023), 1212–1253 DOI

(With Guofang Wei) Examples of open manifolds with positive Ricci curvature and non-proper Busemann functions
to appear in Amer. J. Math., arXiv

Nonnegative Ricci curvature, metric cones, and virtual abelianness
Geom. & Topol. 28 (2024) 1409–1436 DOI

(With Guofang Wei) Examples of Ricci limit spaces with non-integer Hausdorff dimension
Geom. Funct. Anal. 32 (2022) 676-685 DOI

(With Jikang Wang) Some topological results of Ricci limit spaces
Trans. Amer. Math. Soc. 375 (2022), 8445-8464 DOI

Nonnegative Ricci curvature and escape rate gap
J. Reine Angew. Math. 782 (2022) 175-196 DOI

On the escape rate of geodesic loops in an open manifold with nonnegative Ricci curvature
Geom. & Topol. 25 (2021) 1059-1085 DOI

(With Guofang Wei) Semi-local simple connectedness of noncollapsing Ricci limit spaces
J. Eur. Math. Soc. 24 (2022), no. 12, 4027-4062 DOI

Nonnegative Ricci curvature, almost stability at infinity, and structure of fundamental groups

(With Xiaochun Rong) Ricci curvature and isometric actions with scaling nonvanishing property

Nonnegative Ricci curvature, stability at infinity, and finite generation of fundamental groups
Geom. & Topol. 23 (2019) 3203-3231 DOI

A Proof of Milnor conjecture in dimension 3
J. Reine Angew. Math. 758 (2020) 253-260 DOI

Survey Articles

The fundamental groups of open manifolds with nonnegative Ricci curvature
SIGMA 16 (2020), 078, 16 pages DOI (Contribution to Special Issue on Scalar and Ricci Curvature in honor of Misha Gromov on his 75th Birthday)

(with Guofang Wei) Universal covers of Ricci limit and RCD spaces
Differential Geometry in the Large, London Mathematical Society Lecture Note Series (463), Cambridge University Press, 2020, Page 352-372 DOI

Some notes/slides

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.

Nonnegative Ricci curvature and virtually abelian structure file

This short note is about fundamental groups of closed manifolds of zero sectional curvature or non-negative Ricci curvature.

An Invitation to Gromov-Hausdorff convergence slides

Non-academic stuff

US presidential election results in swing states: link

US presidential election results in large metropolitan areas: link

A Duck

Selfie (2021)