Research

I am interested in geometric analysis and geometric partial differential equations. I also have research interests in discrete differential geometry.

My research statement can be viewed here, and a list of publications with abstracts can be viewed here.

Papers

* Denotes undergraduate coauthor

Research Mentoring Experience

I have mentored several undergraduate and graduate students on research problems in differential geometry. Below are links to some of their work.


  • Andrew Marchese and Jacob Miller: Constant Scalar Curvature Metrics on Boundary Complexes of Cyclic Polytopes. (Arizona Summer Program, Summer 2010)
  • Howard Cheng and Peter McGrath: Prescribing Curvature for Piecewise Flat Triangulated 3-manifolds. (Arizona Summer Program, Summer 2010)
  • Veronica Marino: An Introduction to 3-manifolds: A constructive approach. (Research Tutorial Group, Fall 2009)
  • Veronica Marino: Geodesics on Polyhedra. (Masters Thesis, Spring 2010-present)

  • Cindy Phillips: The Geometry of Positively Curved Combinatorial 3-Manifolds. (Research Tutorial Group, Fall 2010)

Geometric Evolutions on Computational Abstract Manifolds (GEOCAM)

Click here for the GEOCAM homepage, where you can find information about our projects and participants.