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.

All Publications

  • Propagation of Singularity with Normally Hyperbolic Trapping Jia, Q. arXiv. 2022 62


    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 Jia, Q., Lin, H. 2020; 61 (5)

    View details for DOI 10.1063/1.5058139

    View details for Web of Science ID 000534016600001

  • 2D Inverse with a Foliation Condition Jia, Q. arXiv. 2020 17


    The inverse problem considers reconstructing functions from some data that are easier to measure, which is typically the integral of that function along geodesics. Our paper proves that if the domain has foliation structure, then this reconstruction process is possible.