my face

Ila Varma

I am an Assistant Professor at UC San Diego.

Previously, I was a NSF Postdoctoral Fellow and Ritt Assistant Professor at Columbia University. Before that, I was a NSF Postdoctoral Fellow at Harvard University in 2015-2016. I received my Ph.D. in September 2015
at Princeton University under the advisement of Manjul Bhargava and Richard Taylor.
 
I'm mainly interested in:
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Contact Info

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Email:
ila at math dot ucsd dot edu
Office: Room 7141 in the AP&M Building
Mailing Address: 9500 Gilman Drive #0112
Mailing Address: La Jolla, CA 92093


Preprints

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


9.
The number of D4-quartic fields ordered by conductor
with Ali Altug, Arul Shankar, and Kevin Wilson
(submitted)

8.
Local-global compatibility for regular algebraic cuspidal automorphic representations when ℓ ≠ p
(submitted)

7.
The mean number of 3-torsion elements in ray class groups of quadratic fields
(submitted)

Papers

6. Differential operators and families of automorphic forms on unitary groups of arbitrary signature
with Ellen Eischen, Jessica Fintzen, and Elena Mantovan
Documenta Mathematica 23 (2018), Pg. 445-495

5.
Odd degree number fields with odd class number
with Wei Ho and Arul Shankar
Duke Mathematical Journal 167 (2018), Number 5, Pg. 995-1047

4.
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

3.
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

2.
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

1.
Finding elementary formulas for theta functions associated to even sums of squares
Indagationes Mathematicae 22 (2011), Issues 1-2, Pg. 12-26


Notes & Miscellanea

a. Sums of Squares, Modular Forms, and Hecke Characters
Master Thesis, Leiden University, June 2010.

b. Kummer, Regular Primes, and Fermat's Last Theorem
Harvard Mathematics College Review, 2 (2008), Issue 2, Pg. 12-24

c. Classification of vector bundles on P^1 over a field via elementary operations on matrices
Lecture Notes, Fall 2009.                                                                                                                                                                       


Teaching

Fall 2018
 Math 100A Section B: Abstract Algebra                                                                                                                      
Fall 2018  Math 204A: Algebraic Number Theory