In December 2007, I received my PhD in mathematics at Duke University. The title of my dissertation is "Cohomology jumping loci and relative malcev completion", which I completed under the direction of my advisor, Richard Hain. My work helps tie together the theory of unipotent completion with that of local system cohomology.
| Office Location: | 025 Physics Bldg |
| Office Phone: | 660-2832 |
| Email Address: | |
| Web Page: | http://math.duke.edu/~nark |
| PhD | Duke University | 2007 |
| BS | Virginia Tech | 2004 |
Current projects: Cohomology jumping loci and relative malcev completion, in preparation for publication, 2008.
I work in the area of algebraic topology, though my research often uses analytic methods such as differential equations and differential forms. I primarily study fundamental groups of topological spaces such as cell complexes and manifolds. In addition, I often study a space by looking at its cohomology with coefficients in local systems. A hyperplane in C^n is a plane which has dimension n-1. For instance, a line in (x,y)-space is a hyperplane. A hyperplane arrangement is a union of hyperplanes in C^n. The complement of this union is of interest to many topologists. In particular, the fundamental group and local system cohomology have particularly interesting properties. In my research, I have developed a tool which can be used to study the fundamental group and is closely related to the local system cohomology.