Hi there! I'm a 1st year postdoctoral fellow at the University of British Columbia. Before this, I was a graduate student at Cornell University from 2015-2020, under the supervision of Ravi Ramakrishna.
For my Phd thesis, I studied the deformation theory of residually reducible Galois representations, motivated by Serre's conjecture for higher rank Galois representations. This led me to develop purely Galois theoretic techniques in deformation theory. My current research interests are summarized as follows.
Galois representations: I explore questions related to the study of Galois representations arising from geometry via purely Galois theoretic methods. The deformation theory of Galois representations plays a significant role in my research.
Iwasawa theory: My research in the subject is motivated the Birch and Swinnerton-Dyer conjecture. I also study the behavior of Iwasawa invariants and their behaviour with respect to congruences.
Arithmetic statistics: Recently, I have formulated a setting in which it is possible to study the average behavior of Iwasawa theoretic invariants for elliptic curves. These results will be considerably strengthened in the future. I'm currently extending this approach to various other contexts of interest in the theory of Galois representations.