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
Transformation Groups vol 27 (2022)
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)
During the Fall 2022 semester, I ran an RIT on parabolic geometries, with joint supervision from Bill Goldman.
The goal of the course was to present Cartan geometries---parabolic geometries in particular---in a more intuitive light,
with a heavy focus on visualization and pictures.
Below are some lecture notes from the course. We ended up focusing largely on understanding the models for Cartan geometries,
but I plan on eventually filling out more of the course, discussing important topics that we weren't able to cover, and then
compiling it into a book.