Jiayin Pan

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

My CV

A Fox

A Duck

Research Interests

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

Research statement

Research Articles

My preprints on arXiv

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

Survey Articles

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

Slides

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

Some notes

Non-Euclidean Geometry file

Lecture notes for Math 113 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.