Jiayin Pan

I am an Assistant Professor at Department of Mathematics, University of California-Santa Cruz.

I received my Ph.D. degree in 2018 from Rutgers Univerisity-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 Postdoctoral Fellowship at Fields Institute during AY 21-22.

Research interests: Global Riemannian geometry, Ricci curvature and topology, Gromov-Hausdorff convergence
Email address: jpan53@ucsc.edu or jypan10@gmail.com
Office: McHenry Library 4178
Office hours: (F22) Monday 3-4 PM, Friday 2-3 PM, or by appointment
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 order they were finished and submitted to arXiv.

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

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

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

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

(With Guofang Wei) Semi-local simple connectedness of noncollapsing Ricci limit spaces, J. Eur. Math. Soc. DOI.

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

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

(With Jikang Wang) Some topological results of Ricci limit spaces, arXiv, to appear in Trans. Amer. Math. Soc.

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

Nonnegative Ricci curvature, metric cones, and virtual abelianness, arXiv, to appear in Geom. & Topol.

(With Guofang Wei) Examples of open manifolds with positive Ricci curvature and non-proper Busemann functions, arXiv

(With Xianzhe Dai, Shouhei Honda, and Guofang Wei) Singular Weyl’s law with Ricci curvature bounded below, arXiv

Survey Articles

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

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

Some notes/slides

Non-Euclidean Geometry file

Lecture notes for undergraduate course Non-Euclidean geometry. We loosely follow the textbook Geometries and Groups by Nikulin and Shafarevich. Most proofs have been rewritten and more content has been added. This note is self-contained.

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. It includes Buser’s proof on classical Bieberbach’s theorem and Cheeger-Gromoll’s proof on virtually abelian structure. It also offers a viewpoint of virtual abelianness from virtual nilpotency.

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)