#  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](/file_url/145) 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](/file_url/144) for Phd Work).

I organize [Harvard CMSA weekly Mathematical General Relativity](https://cmsa.fas.harvard.edu/events-archive/category/general-relativity/) seminar series. See the [website](https://cmsa.fas.harvard.edu/events-archive/category/general-relativity/) for detail.

 Some highlights from Fall 2024 General Relativity Seminar

 **Christoph Kehle (MIT)** on the [disproof of the third law of black hole thermodynamics](/file_url/146)

 **Marcelo Disconzi (Vanderbilt)** on the [free boundary problem in Einstein-Euler system](/file_url/147)

 **Tin Yau Tsang (MSRI Berkeley)** on a [mass for large and small in relativity](/file_url/148)

 **Xuantao Chen (Johns Hopkins)** [on a new proof of the formation of a trapped surface in geodesic foliation](/file_url/149)

 **Nikos Athanasiou (ACT Greece)** On the first result on [the large data problem in Einstein-Vlasov system in the absense of any symmetry](/file_url/150), See [here ](https://www.youtube.com/watch?v=gtvSMhYhD3w&t=3415s)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](https://www.youtube.com/watch?v=2k_YbipgEuo)