I completed my undergraduate degree in Pure Mathematics in 1998; I studied at the Faculty of Mathematics of the University of Belgrade in what was then the Federal Republic of Yugoslavia.
I came to University of Oregon in 1999 to work on my PhD degree under the direction of Prof. Peter B. Gilkey. I defended my PhD thesis, "Spectral Geometry of the Riemann Curvature Tensor", in 2003.
Spectral geometry of the Riemann curvature tensor remains to be one of my interests. It examines the geometric condition imposed when a family of operators associated to the curvature tensor is assumed to have constant spectrum or constant Jordan normal form on the appropriate domain of definition. This is motivated at least in part by the study of locally isotropic pseudo-Riemannian manifolds. The techniques used in my work are often from algebraic topology: bundle theory and characteristic classes.
In the last two years I spent most of my research time on general relativity and the field of Einstein constraint equations. Roughly speaking, solutions of the Einstein constraint equations can be though of the "spatial" geometry of our "universe" at a "particular moment in time". I am involved in two gluing projects in which new solutions of the constraints are built form "old" solutions. The mathematics involved in these projects is essentially elliptic PDE's (on three-dimensional Riemannian manifolds).
I am also interested in projective geometries whose isometry groups are exceptional Lie Groups. More specifically, I have been working with undergraduates on the (semi-)Riemannian geometry of (para-)octonionic projective planes.
My publications include:
Created by: Iva Stavrov, istavrov [at] lclark [dot] edu
Updated: October 11th 2006
