## Colin M. Lawson Ph.D. Student in MathematicsUniversity of North Texas

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.

## Teaching

• Spring 2020: Recitation Instructor for Math 1710; TTR 8 - 8:50am and 9 - 9:50am
• Office Hours: TTR 10:30-11:30am
• Fall 2019: Instructor for Math 0340.006; MWF 2 - 3:50pm
• Office Hours: Mondays 9:30-10:30am and Fridays 10:30-11:30am

## 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.

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

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