I am an assistant professor at Department of Mathematics, Northeastern University. In Fall 2019 I was a Uhlenbeck Postdoctoral Fellow in
MSRI Microlocal Analysis Program. I obtained my PhD from MIT in 2015.
Here is my
My research is partially supported by NSF Grant
Geometric analysis, microlocal analysis, partial differential equations, mathematical physics.
Publications and Preprints:
Fundamental gaps of spherical triangles. Joint with Shoo Seto and Guofang Wei.
Spectral 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.
New York Journal of Mathematics 26 (2020) 272--284. Journal version
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.
Geometry and Topology 24 (2020) 309–372. Journal version
Boundary behaviour of Weil-Petersson and fiber metrics for Riemann moduli spaces. Joint with Richard Melrose.
International Mathematics Research Notices, Volume 2019, Issue 16, Pages 5012–5065. Journal version
Eleven dimension supergravity equations on edge manifolds.
Annales Henri Poincaré, Volume 19, Issue 8 (2018), 2347–2400. Journal version
Eigenvalue resolution of self-adjoint matrices.
Pacific Journal of Mathematics, Vol. 288 (2017), No. 1, 241–255. 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 The eleven dimensional supergravity equations, resolutions and Lefschetz fiber metrics.
Talk Slides and Videos:
An introduction to pseudodifferential operators.
Videos of my minicourse at MSRI:
(Photo by David Eisenbud)
A (very gentle) introduction to blow ups and applications to geometry.
video of my talk at MSRI.
Constant curvature conical metrics.
Oberwolfach Report No. 30/2019, DOI: 10.4171/OWR/2019/30.