Exploring the Grand Canyon, Summer 2017

Colin M. Lawson
Ph.D. Student in Mathematics
University of North Texas

General Academic Bldg., Room 478
Email: ColinLawson@my.unt.edu

"Do not allow watching food to replace making food."

-Alton Brown

I'm a fourth year Ph.D. student at the University of North Texas, advised by Dr. Anne Shepler. I use Hochschild cohomology to find deformations of skew group algebras over fields acting in positive characteristic.

Curriculum Vitae


Research Interests

I currently work in algebraic deformation theory where I use techniques from homological algebra. If A is an algebra, then the idea is perturb the multiplication in the algebra slightly with parameter $t$. The multiplication is the resulting algebra may or may not be associative. I also enjoy learning about the history of homological algebra, in particular, the history leading up to Hochschild cohomology (because this is what I compute most) to deformation theory. The journey from Riemann & Betti to Noether and from Eilenburg & MacLane to Hochschild, Gerstenhaber and Schack is an interesting one.

This is my favorite chain complex.

$\begin{equation}\label{relative-bar} \cdots \stackrel{\delta_3}{\longrightarrow} A\otimes A\otimes A\otimes A \stackrel{\delta_2}{\longrightarrow} A\otimes A\otimes A \stackrel{\delta_1}{\longrightarrow} A\otimes A \stackrel{\delta_0}{\longrightarrow} A\rightarrow 0 \end{equation}$

$\delta_0(a \otimes b)=ab$
$\delta_1(a \otimes b \otimes c)=ab \otimes c - a \otimes bc$
$\delta_2(a \otimes b \otimes c \otimes d)=ab \otimes c \otimes d - a \otimes bc \otimes d + a \otimes b \otimes cd$

Camping & Road Trips

I grew up in Sabinal, TX -- a very small town about an hour and a half west of San Antonio, along Hwy 90. I spent a lot of time outside in the hill country, so between semesters, I try to take either a short camping trip or a road trip. Sometimes it's nice to leave my computer at home and get away from the city lights. Here are some of my most recent trips.

Other links

Mathematics Graduate Student Seminar (MGS)