## Marshall Hampton's Homepage

#### "I have traveled a good deal in Concord" -Thoreau

Office: Solon Campus Center (SCC) 172

Email: mhampton at d.umn.edu

Department of Mathematics and Statistics
University of Minnesota Duluth
Solon Campus Center 140
1117 University Drive
Duluth, MN 55812-3000

### Courses:

Summer 2013:

Math 3280: Introduction to Differential Equations and Linear Algebra.

Spring 2013:

Math 5233: Mathematical Foundations of Bioinformatics.

My academic family tree. This is much better than my old version, which I did by hand. This updated one includes many more nodes, due to updates at the Mathematics Genealogy Project and it uses David Alber's excellent program Geneagrapher.

CV   Feel free to email me a request for electronic copies of papers/preprints.

### Research:

Currently I am split between two very different arenas:
(1) using computational algebra and geometry to study special solutions (usually relative equilibria) of the n-body and n-vortex problem,

and

(2) mathematical biology of gene regulation, particularly that involved in mammalian hibernation with the research group of Matthew Andrews. Recently I have become interested in cardiovascular modeling in the context of hibernation.
From using it as an example in my bioinformatics courses, I have become interested in the biology and genome of the Plasmodium parasites that cause malaria. This is becoming a third branch of my strange research tree, but I spend most of my time working on the first two.

I use the free, open-source program/environment Sage in all of my work; I encourage you to try it and contribute to it if you can.
Here are a few pages of images, animations, and other possibly interesting stuff that relates to research I have done or am doing:

Newton polytopes for the restricted four-body problem

Lagrange central configuration animation

Four body collinear central configuration, on elliptical orbits of eccentricity .8 (masses are 1,2,3,4).

A non-regular Groebner fan, found by Anders Jensen. I have done some work integrating Jensen's program Gfan into Sage. The graphical capabilities of Sage make some interesting visualizations possible.

The 600-cell, a regular polytope in 4 dimensions with 600 3d cells (faces). Recently I have tried to add some polytope functions to Sage, although the much more powerful polymake is the best program for that, and is an optional Sage package.

3D slices through the 600-cell (mp4 movie, 4.5 MB).

Minkowski sums of platonic solids (mp4 movie, 26.4 MB).

A movie of reflective spheres. The light rays that are trapped in the center of the four spheres form an interesting fractal.

I am working on a "Mathematical Coloring Book"; you can buy a prototype at cost at lulu.com, or download the pdf for free. The lulu printed copy is pretty nice; they are cheaper if you buy 25 or more at a time.
I have a blog which, unless you are a very unusual person, you will not find interesting.