News (July 2021): Three new papers on the characteristic gluing problem for the Einstein equations! In collaboration with Stefanos Aretakis and Igor Rodnianski.
- The characteristic gluing problem for the Einstein equations and applications (31 pages, arXiv:2107.02441)
- The characteristic gluing problem for the Einstein vacuum equations. Linear and non-linear analysis (102 pages, arXiv:2107.02449)
- Characteristic gluing to the Kerr family and application to spacelike gluing (88 pages, arXiv:2107.02456)
In my research I use tools from analysis, PDE theory and differential geometry to study fundamental questions of general relativity. With my collaborators I investigate the following mathematical research topics:
- Spacelike constraint equations (construction and extension procedures, asymptotic analysis).
- Null structure equations (construction and control of solutions, sharp estimates in geometric function spaces).
- Control of the Einstein Equations at the low-regularity level of L2-curvature (continuation results, blow up criteria).
- Asymptotic analysis of spacetimes.
- Gluing problems for characteristic and spacelike initial data.
My publications and preprints can be found on the research page.
The background picture above depicts the star cluster NGC 2203, credits go to ESA/Hubble.