my face

Ila Varma

I am an Assistant Professor at University of Toronto

Previously, I was an Assistant Professor at UC San Diego. Before that, I was a NSF Postdoctoral Fellow at Columbia University and Harvard University. 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:

UofTCensure - What did we achieve?

Day of Refusal to Demand Cops off Campus Resources

#ScholarStrike Resources

ShutdownSTEM Resources

Is this who we are, academia? - by Amanda Lehr and Tatiana McInnis

Contact Info
ila at math dot toronto dot edu
Office: Room 6108 in the Bahen Centre
Mailing Address: Dept. of Mathematics
Mailing Address: Bahen Building
Mailing Address: 40 St. George Street
Mailing Address: Toronto, ON M5S 2E4


11. Geometry-of-numbers methods in the cusp and applications to class groups
with Arul Shankar, Artane Siad, and Ashvin Swaminathan

10. On unit signatures and narrow class groups of odd abelian number fields: structure and heuristics
with Ben Breen and John Voight
(including an appendix with Noam Elkies)
(accepted, to appear in Transactions of the American Mathematical Society)

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
(accepted, to appear in the Israel Journal of Mathematics)


7. The number of D4-quartic fields ordered by conductor
with Ali Altug, Arul Shankar, and Kevin Wilson
Journal of the European Mathematical Society (JEMS) 23 (2021), Number 8, Pg. 2733-2785

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

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

p-adic q-expansion principles on unitary Shimura varieties
with Ana Caraiani, Ellen Eischen, Jessica Fintzen, and Elena Mantovan
Directions in Number Theory 3 (2016), Springer, Pg. 197-244

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

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

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.


Current Teaching
Fall 2021
MAT 1100: Algebra
Fall 2021
MAT 495: Algebraic Number Theory
Fall 2021
MAT 224: Linear Algebra II

Fall 2020
MAT 415/MAT 1200: Algebraic Number Theory
Fall 2020
MAT 224: Linear Algebra II

Fall 2019
MAT 477: Seminar in Mathematics
Fall 2019
MAT 224: Linear Algebra II
UC San Diego
 Math 109: Mathematical Reasoning                                                                                                                      
Fall 2018
 Math 100A: Abstract Algebra                                                                                                                      
Fall 2018  Math 204A: Algebraic Number Theory         
Columbia University
Fall 2017
 Math 1101: Calculus I
Fall 2016
 Math 1101: Calculus I
Princeton University
Fall 2013
 MAT 104: Calculus II