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## 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:
 Office Location: 025 Physics Office Phone: 660-2832 Email Address: Web Page: http://math.duke.edu/~nark

Education:

 PhD Duke University 2007 BS Virginia Tech 2004
Specialties:

Topology
Research Interests: Algebraic Topology, Hyperplane Arrangements, Local System Cohomology

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.

Keywords:

Topology • Algebraic • Hyperplanes • Arrangements • Local • System • Cohomology • Completion

Curriculum Vitae
Recent Publications

1. A.J. Narkawicz, Cohomology jumping loci and relative malcev completion (Preprint, 2008)

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320