Research

My research centers on analysis and Partial Differential Equations (PDEs), utilizing techniques from harmonic analysis to rigorously study PDEs that arise in differential geometry, mathematical physics (relativity) and, more recently, mathematical biology. Within the realm of analysis, I am focused on constructing solutions to geometric evolution equations and investigating the dynamics of both regular and singular solutions. Additionally, I aim to understand scalar curvature rigidity problems in comparison geometry and explore geometric flows to elucidate morphogenesis in mathematical biology, as well as address the Riemannian and Lorentzian Penrose inequalities using spinor methods. I am also interested in low dimensional geometry and topology in particular Teichmuller theory that arises naturally in mathematical general relativity and string theory-check here for Ph.D work. Another application that I am interested in is mathematically rigorously studying geophysical phenomena such as non linear elastic wave propagation through heterogeneous and anisotropic medium (propagating seismic waves through planet's interior- check here for Phd Work).

I organize Harvard CMSA weekly Mathematical General Relativity seminar series. See the website for detail. 

 Some highlights from Fall 2024 General Relativity Seminar

     Christoph Kehle (MIT) on the disproof of the third law of black hole thermodynamics

     Marcelo Disconzi (Vanderbilt) on the free boundary problem in Einstein-Euler system

     Tin Yau Tsang (MSRI Berkeley) on a mass for large and small in relativity

    Xuantao Chen (Johns Hopkins) on a new proof of the formation of a trapped surface in geodesic foliation

    Nikos Athanasiou (ACT Greece) On the first result on the large data problem in Einstein-Vlasov system in the absense of any symmetry, See here  for the video.

Spring 2025 General Relativity Seminar:

Liam Urban (Vienna) on On the past maximal development of near-FLRW data for the Einstein scalar-field Vlasov system