Hi there! I'm a postdoctoral fellow at the University of British Columbia. I specialize in number theory and arithmetic geometry. Before this, I was a graduate student at Cornell University from 2015-2020, under the supervision of Ravi Ramakrishna.
Here is a link to my papers on the arxiv.
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: In the context of arithmetic statistics, I realized how to formulate a setting in which it is possible to study the average behavior of Iwasawa theoretic invariants for elliptic curves. This approach builds on ideas from some of my earlier work on Euler characteristics in Iwasawa theory. My motivation was to study the variation of Iwasawa invariants for elliptic curves that are ordered by height. This approach has now been extended in the generality of noncommutative Iwasawa theory.
UCLA Number theory seminar, 1 Nov.
CMS Winter session: Galois representations and L-functions, 4-5 Dec.
CMS Winter session: Algebraic number theory, 4-5 Dec.
Organization this semester:
Contact: email: firstname.lastname@example.org
photo credit: Melissa Totman