I am a visiting assistant professor at the Department of Mathematics, University of California-Santa Barbara, since 2018 Fall.

I received my Ph.D. degree in 2018 from Rutgers Univerisity-New Brunswick, advised by Xiaochun Rong.

**Email address:** j_pan@math.ucsb.edu or jypan10@gmail.com

**Office:** South Hall 6723

Riemannian geometry, Ricci curvature and topology, Gromov-Hausdorff convergence

The articles are listed in the order they were finished and submitted to arXiv. Click here for more details on these articles.

*A Proof of Milnor conjecture in dimension 3,* **J. Reine Angew. Math.** 758 (2020) 253–260. DOI 10.1515/crelle-2017-0057

*Nonnegative Ricci curvature, stability at infinity, and finite generation of fundamental groups,* **Geom. & Topol.** 23 (2019) 3203–3231. DOI 10.2140/gt.2019.23.3203

*Ricci curvature and isometric actions with scaling nonvanishing property* (with Xiaochun Rong), arXiv:1808.02329

*Nonnegative Ricci curvature, almost stability at infinity, and structure of fundamental groups,* arXiv:1809.10220

*Semi-local simple connectedness of noncollapsing Ricci limit spaces* (with Guofang Wei), arXiv:1904.06877, to appear in **J. Eur. Math. Soc.**

*On the escape rate of geodesic loops in an open manifold with nonnegative Ricci curvature,* **Geom. & Topol.** 25 (2021) 1059–1085 DOI: 10.2140/gt.2021.25.1059

*Nonnegative Ricci curvature and escape rate gap,* arXiv:2009.00226

*Some topological results of Ricci limit spaces* (with Jikang Wang), arXiv:2103.11344

*The fundamental groups of open manifolds with nonnegative Ricci curvature*

SIGMA 16 (2020), 078, 16 pages https://doi.org/10.3842/SIGMA.2020.078

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 link

Here are some of my slides for talks.

*Semi-local simple connectedness of non-collapsing Ricci limit spaces* slide

*On the escape rate of geodesic loops in an open manifold of nonnegative Ricci curvature* slide youtube bilibili

*Non-Euclidean Geometry* file

Lecture notes for Math 113 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.