I am a Morrey Visiting Assistant Professor in mathematics. In Fall 2019 I am a Uhlenbeck Postdoctoral Fellow in MSRI Microlocal Analysis Program. Here is my CV.
My research is partially supported by NSF Grant DMS-1905398.
- Geometric analysis, microlocal analysis, partial differential equations, mathematical physics.
Publications and Preprints:
Specctral properties of reducible conical metrics. Joint with Bin Xu.
arXiv: 1909.00546. Submitted.
Conical metrics on Riemann surfaces, II: spherical metrics. Joint with Rafe Mazzeo.
arXiv: 1906.09720. Submitted.
- Rigidity of a family of spherical conical metrics.
arXiv: 1902.02024. Submitted.
- Spherical conic metrics and realizability of branched covers.
Proceedings of the AMS, Volume 147, Number 4, April 2019, Pages 1805–1815. Journal version
- Conical metrics on Riemann surfaces, I: the compactified configuration space and regularity. Joint with Rafe Mazzeo.
Accepted by Geometry and Topology.
- Eleven dimension supergravity equations on edge manifolds.
Annales Henri Poincaré, Volume 19, Issue 8 (2018), 2347–2400. Journal version
- Boundary behaviour of Weil-Petersson and fiber metrics for Riemann moduli spaces. Joint with Richard Melrose.
International Mathematics Research Notices, Vol. 2017, No. 00, pp. 1–54. Journal version
- Resolution of the canonical fiber metrics for a Lefschetz fibration. Joint with Richard Melrose.
Journal of Differential Geometry, Volume 108, Number 2 (2018), 295-317. Journal version
- Eigenvalue resolution of self-adjoint matrices.
Pacific Journal of Mathematics, Vol. 288 (2017), No. 1, 241–255. Journal version
- The eleven dimensional supergravity equations, resolutions and Lefschetz fiber metrics. PhD thesis
Talk Slides and Videos:
An introduction to pseudodifferential operators.
Videos of my minicourse at MSRI: I, II.
(Photo by David Eisenbud)
A (very gentle) introduction to blow ups and applications to geometry.
A video of my talk at MSRI.
- Constant curvature conical metrics.
Oberwolfach Report No. 30/2019, DOI: 10.4171/OWR/2019/30.