my face

Ila Varma

I am a NSF Postdoctoral Fellow and Ritt Assistant Professor at Columbia University. Previously, I was a NSF Postdoctoral Fellow at Harvard University. Before that, I was a graduate student at Princeton University under the advisement of Manjul Bhargava and Richard Taylor. Here is my CV.

I'm mainly interested in:

Contact Info

Email: ila at math dot columbia dot edu
Office: Room 517 in the Mathematics Building, Columbia University
Mailing Address: MC 4436, 2990 Broadway, New York, NY 10027


Crystallinity of Galois representations associated to regular algebraic cuspidal automorphic representations of GLn
(in preparation)

The number of D4-quartic fields ordered by conductor
with Ali Altug, Arul Shankar, and Kevin Wilson
arXiv logo
Local-global compatibility for regular algebraic cuspidal automorphic representations when ℓ ≠ p
The mean number of 3-torsion elements in ray class groups of quadratic fields
Odd degree number fields with odd class number
with Wei Ho and Arul Shankar
(to appear in Duke Mathematical Journal)
Differential operators and families of automorphic forms on unitary groups of arbitrary signature
with Ellen Eischen, Jessica Fintzen, and Elena Mantovan
(to appear in Documenta Mathematica)


arXiv logo
p-adic q-expansion principles on unitary Shimura varieties
with Ana Caraiani, Ellen Eischen, Jessica Fintzen, a
nd Elena Mantovan
Directions in Number Theory 3 (2016), Springer, Pg. 197-244
Arxiv logo The mean number of 3-torsion elements in the class groups and ideal groups of quadratic orders
Manjul Bhargava
Proceedings of the London Mathematical Society 112 (2016), Issue 2, Pg. 235-266
Arxiv logo On the mean number of 2-torsion elements in the class groups, narrow class groups, and ideal groups of cubic orders and fields
with Manjul Bhargava
Duke Mathematical Journal 164 (2015), Number 10, Pg. 1911-1933
arXiv logo
Finding elementary formulas for theta functions associated to even sums of squares
Indagationes Mathematicae 22 (2011), Issues 1-2, Pg. 12-26

Notes & Miscellanea

PDF logo Sums of Squares, Modular Forms, and Hecke Characters
Master Thesis, Leiden University, June 2010.
PDF logo Kummer, Regular Primes, and Fermat's Last Theorem
Harvard Mathematics College Review, 2 (2008), Issue 2, Pg. 12-24
PDF logo Classification of vector bundles on P^1 over a field via elementary operations on matrices
Lecture Notes, Fall 2009.