Current Research and Scholarly Interests
My research focuses on inverse problems and propagation of
singularities using microlocal analysis.
Regarding the propagation of singularity, I currently focus on the Einstein equation on Kerr de-Sitter spacetimes.
Propagation of Singularity with Normally Hyperbolic Trapping
We prove a new microlocal estimate with normally hyperbolic trapping, which can be applied to Kerr-de Sitter spacetimes. We use a new type of symbol class, and corresponding operator class, which is constructed by blowing up the intersection of the unstable manifold and the fiber infinity. The extra loss of the microlocal estimates compared with the standard propagation of singularities is arbitrarily small.
- Calabi-Yau generalized complete intersections and aspects of cohomology of sheaves JOURNAL OF MATHEMATICAL PHYSICS 2020; 61 (5)
- 2D Inverse with a Foliation Condition arXiv. 2020 17