Anthony J. Narkawicz, Graduate Student
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.
Please note: Anthony has left the Mathematics department at Duke University; some info here might not be up to date.
- Contact Info:
- Research Interests: Algebraic Topology, Hyperplane Arrangements, Local System Cohomology
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.
- Topology • Algebraic • Hyperplanes • Arrangements • Local • System • Cohomology • Completion
- Curriculum Vitae
- Recent Publications
- A.J. Narkawicz, Cohomology jumping loci and relative malcev completion