Colton Sandvik

Department of Mathematics

Louisiana State University

Office: Lockett 379

Notes

Notes on Character Sheaves. Some (very) incomplete notes on character sheaves that I wrote while trying to learn the subject. I hope to update these as I find the time. Beware they are most surely riddled with typos, inaccuracies, and incomplete arguments and ideas.

Singular Support and Representation Theory for the Working Differential Geometer. Some in-progress notes on singular support of constructible sheaves for manifolds and étale constructible sheaves on algebraic varieties for an two upcoming talks in the LSU Informal Geometry and Topology seminar. The section on singular support for étale constructible sheaves is still incomplete. These notes are written for an audience with no assumed familiarity with the notion of a sheaf, so one should have abundant caution when reading them.

Spherical Buildings and Tit's Simplicity Theorem. My Honors Thesis from the University of Oklahoma under the supervision of Prof. Alan Roche. In this paper, I present an exposition on buildings and provide an elementary proof of Tits simplicity theorem.

Weyl Groups and Symmetries of Solids. My Capstone Paper from the University of Oklahoma on Weyl Groups and viewing them as symmetry groups of solids.

Software

Pieri's. A python library for computing the cohomology ring structure of the Grassmannian using Schubert calculus. It is an implementation of Pieri's formula and Giambell's formula. This was made as a fun project during the Algebra VIR on Enumerative Geometry at LSU in Spring 2022.

Algebras Don't Lie. A web server / page which embeds some sage code to provide some visualizations of root systems on Lie algebras. This was developed independently in a continuous 24 hour period (along with another project) for the hackathon, Hacklahoma, in Feburary of 2020. I am not entirely sure if it even still runs, but it was a lot of fun making.

Math is Beautiful. A web server / page for performing fun visualizations of functions. One specifies RGB values using functions of the coordinates x,y on the plane. The program will then produce an image using these functions. This is of little math importance, and mostly exists as a fun tool to encourage a wider audience that math is truly beautiful, engaging, and fun. This was developed in a continuous 24 hour period (along with two other projects) for the hackathon, Hacklahoma, in February of 2019. As a result, it is not great code by any means, and may be hard to setup.

Other

Penrose Cookies. A collection of 3D printable files for producing cookie cutters for Sir. Roger Penrose's P1 tiling of the plane. This also includes the SCAD file for making the STL models, so they can be easily altered as one desires. I recommend a sugar cookie with different colored icing for each of the shapes, and an ample selection of different teas to enjoy with

Two-Sided Cells. A collection of pictures containing the two-sided cells for various finite Weyl groups. It includes both the ordinary two-sided cells along with the two-sided p-cells. The choices for p were based on the possible torsion, so it should include all the interesting cases for Weyl groups associated with root systems of rank 5 and smaller.