Jacob W. Erickson
CV available here, last updated September 10, 2022
I'm a graduate student at the University of Maryland, College Park, studying under
Bill Goldman and Karin Melnick.
I'm interested in Lie groups, Cartan geometries,
and locally homogeneous geometric structures.
Papers
- Closed surfaces with maximal local rolling symmetries
In preparation
This is my thesis.
- A stitching theorem for maps between Cartan geometries
In preparation
This will be a paper on the "stitching theorem" that I used in conjunction with sprawls
to prove that higher-order fixed points force compact projective geometries to be isomorphic to the Klein
geometry, if you went to Strasbourg and are wondering where it is.
- A method for determining Cartan geometries from the local behavior of automorphisms
In preparation
This is the "sprawl paper", if you went to Strasbourg and are wondering where it is.
- Higher rank parabolic geometries with essential automorphisms and nonvanishing curvature
Submitted
arXiv preprint
- Intrinsic holonomy and curved cosets of Cartan geometries
European Journal of Mathematics vol 8, 446-474 (2022)
arXiv preprint
"Parabolic Geometries for People that Like Pictures"
(aka the Parabolic Geometries RIT)
This semester, I'm running an RIT on parabolic geometries, jointly supervised by Bill Goldman.
The goal of the course is to thoroughly disprove the idea that Cartan geometries---parabolic
geometries in particular---are unintuitive by actually explaining the geometric intuition behind
Cartan geometries.
The lecture notes from the course are available below.