Research
I am interested in geometric analysis and geometric partial differential equations. In particular, I am currently studying Ricci flow, Yang-Mills heat flow and the cross curvature flow.
My research statement can be viewed here, and a list of publications with abstracts
can be viewed here.
Papers
- "Ricci Yang-Mills Solitons on Nilpotent Lie Groups" with Michael Jablonski (submitted)
- "The Cross Curvature Flow on a Negatively Curved Solid Torus" with Dan Knopf and Jason Deblois (submitted)
- "Asymptotic Stability of the Cross Curvature Flow at a Hyperbolic Metric" with Dan Knopf (to appear in Proc. Amer. Math. Soc. )
- "Modified Ricci Flow on a Principal Bundle" my Ph.D. thesis
- "Stability of the Ricci Yang-Mills flow at Einstein Yang-Mills metrics" (submitted)