Jiayin Pan

I am currently a postdoctoral fellow at the Fields Institute for the 2021-2022 academic year.

I received my Ph.D. degree in 2018 from Rutgers Univerisity-New Brunswick, advised by Xiaochun Rong. I was a Visiting Assistant Professor at the Department of Mathematics, University of California-Santa Barbara, during the 2018-2021 academic years.

Starting in Fall 2022, I will be an Assistant Professor at the Department of Mathematics, University of California-Santa Cruz.

Research interests: Global Riemannian geometry, Ricci curvature and topology, Gromov-Hausdorff convergence
Email address: jypan10@gmail.com or jpan@fields.utoronto.ca
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 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), J. Eur. Math. Soc. DOI:10.4171/JEMS/1166.

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, J. Reine Angew. Math. DOI:10.1515/crelle-2021-0065

Some topological results of Ricci limit spaces (with Jikang Wang), arXiv:2103.11344, to appear in Transactions of the AMS

Examples of Ricci limit spaces with non-integer Hausdorff dimension (with Guofang Wei), Geom. Funct. Anal. DOI:10.1007/s00039-022-00598-4

Nonnegative Ricci curvature, metric cones, and virtual abelianness, arXiv:2201.07852

Examples of open manifolds with positive Ricci curvature and non-proper Busemann functions (with Guofang Wei), arXiv:2203.15211

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

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

An accessible talk that I gave at the Fields Institute.
Abstract: We give an introduction to the notion of Gromov-Hausdorff convergence. The Gromov-Hausdorff distance between two metric spaces measures how they look alike. We will talk about how this notion was used by Gromov to solve a problem in geometric group theory and how it revolutionized modern Riemannian geometry.

Non-academic stuff

US presidential election results in swing states: link

US presidential election results in large metropolitan areas: link

A Duck

Selfie (2021)