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

Preprints



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

arXiv
                      logo
The number of D4-quartic fields ordered by conductor
with Ali Altug, Arul Shankar, and Kevin Wilson
(submitted)
arXiv logo
Local-global compatibility for regular algebraic cuspidal automorphic representations when ℓ ≠ p
(submitted)
arXiv
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The mean number of 3-torsion elements in ray class groups of quadratic fields
(submitted)
arXiv
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Odd degree number fields with odd class number
with Wei Ho and Arul Shankar
(to appear in Duke Mathematical Journal)
arXiv
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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)

Papers

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
with
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.