### Research Focus

Differential Geometry and Geometric Analysis

The broad area of my research is geometric analysis, which deals with various partial differential equations that arise in geometry. I am particularly interested in the prescribed Ricci curvature equation and the Einstein equation.

Since these partial differential equations are often exceedingly difficult to study, my research focuses on cases where the underlying geometry enjoys certain symmetries and the equations simplify.

Specifically, I consider homogeneous and cohomogeneity one spaces, on which the equations reduce to systems of algebraic equations and ordinary differential equations respectively.

### Publications

- The Dirichlet problem for Einstein metrics on cohomogeneity one manifolds, Ann. Glob. Anal. Geom., 54(1):155--171, 2018.
- Cohomogeneity one quasi-Einstein metrics, J. Math. Anal. Appl., 470(1):201--217, 2019.
- On the Ricci iteration for homogeneous metrics on spheres and projective spaces (with A. Pulemotov, Y. Rubinstein and W. Ziller),. Submitted, arXiv:1811.01724.
- Local Stability of Einstein Metrics Under the Ricci Iteration (with M. Hallgren). Submitted, arXiv:1907.10222.