my face

Ila Varma

I am an Assistant Professor at University of Toronto. I am currently a Sloan Research Fellow (2020 - present) and have been awarded the Connaught Research Fund (2021-2022). I am also a former Fulbright Scholar to the Netherlands.

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:

UofT Mathematics Department's Equity Forum


Day of Refusal to Demand Cops off Campus

#ScholarStrike - led by Dr. Anthea Butler and Dr. Kevin Gannon occurred on September 2020

ShutdownSTEM Resources - occurred in June 2020

Is this who we are, academia? by Amanda Lehr and Tatiana McInnis - June 2020

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


12. Power-saving error terms for the number of D4-quartic extensions over a number field ordered by discriminant
with Alina Bucur, Alexandra Florea, Allechar Serrano Lopez
11. Geometry-of-numbers methods in the cusp
with Arul Shankar, Artane Siad, and Ashvin Swaminathan

10. Local-global compatibility for regular algebraic cuspidal automorphic representations when ℓ ≠ p
(accepted, to appear in Forum of Mathematics Sigma)


9. 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)
Transactions of the American Mathematical Society Series B, 10 (2023), Pg. 86-128

The mean number of 3-torsion elements in ray class groups of quadratic fields
Israel Journal of Mathematics 252 (2022), Pg. 149-185
Since publishing this article, I have taken time to reflect on Zionism, Hindu Nationalism, and White Supremacy/Christian Nationalism, and I no longer believe that it was okay to be so concerned with my own career to publish and therefore uphold the Zionist settler-colonial state of Israel. Since then, I have signed the US Campaign for the Academic and Cultural Boycott of Israel, USACBI. I urge all mathematicians to do the same as me. I apologize to all Palestinians (as well as all anti-Zionists) for this oversight. If you would like to learn more about the Boycott, especially as a mathematician, please read the Just Mathematics Collective's USACBI Statement.
From the river to the sea, Palestine will be free

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

Past Teaching
Fall 2023 MAT 1210: Class Field Theory

Fall 2022
MAT 1100: Algebra

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