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

CV

Besides mathematics, I enjoy reading election analysis, playing Metroidvania and puzzle games, and hiking.

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

*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

*Non-Euclidean Geometry* file

Lecture notes for undergraduate course Non-Euclidean geometry. We loosely follow the textbook

Geometries and Groupsby 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

US presidential election results in swing states: link

US presidential election results in large metropolitan areas: link