Aaron Wangberg

Full Professor
Department of Mathematics & Statistics
Winona State University

Office: Stark 203I
Phone: (507) 474-5777
E-mail: awangberg@winona.edu
Postal address:
Department of Mathematics
Winona State University
175 W. Mark St.
Winona, MN 55987
Luther College, Iowa, B.A., May 2001
Oregon State University, Ph.D., Fall 2007

Competing with 9,000 triathletes at the 2006 Wildflower Olympic Triathlon at Lake San Antonio, California. (I'm in the lower right.)


Fall 2007
Math 260: Multivariable Calculus, MTThF 10:00-10:50
Math 140: Applied Calculus, MWF 11:00-11:50
Math 110: Finite Mathematics, TTh 2:00-3:20
Office hours:
Monday Tuesday WednesdayThursdayFriday
12:00 - 2:00 11:00 - 12:30 None 11:00 - 12:30 8:00am-10:00am
3:30 - 5:00 3:30 - 5:00
Teaching Philosophy
A list of previous teaching experiences
Information about various teaching projects:
The Bridge Project Multivariable Calculus Labs
Math Excel Making Connections Course Flier
Graduate Teaching Seminar Syllabus


Research interests
My research interests are in Lie groups and non-associative algebras. In particular, I study the subgroup structure of E6 using an explicit construction involving the octonions. The commutation table can be found here.
My advisor is Professor Tevian Dray
My curriculum vitae
My research statement
Here's a brief list of possible undergraduate research projects

The figure to the right is the root diagram for the 52 dimensional Lie algebra F4. There are 48 non-zero vertices and 48 independently oriented edges, or roots, each corresponding to a different element of the algebra. The remaining 4 elements live at the origin. Every vertex in the diagram can be reached by adding together particular combinations of four positive roots.

Count the number of vertices... Try it! Take the mouse, grab the picture, and turn it around. How many vertices do you see?

You won't get 48 -- only 32 and the origin! That's because F4 lives in four dimensions, and to get a diagram we can visualize in three dimensions, we must project along one special direction. For this diagram, we've projected along the first simple root -- That is, we've projected F4. If you choose the right projection, the diagram can be interpretted as corresponding to a subalgebra of F4. In fact, you can visually identify an algebra's subalgebras using its root diagram.

Here's an animation of the root diagram for F4 where we've choosen to project along a direction that smoothly changes from the first simple root to the fourth. You can play the animation and simultaneously turn the figure, and in the meantime, test your knowledge of four dimensions!

This page was last updated: October 2, 2007