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-present).

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:

Rehumanizing mathematics
Arithmetic statistics--in particular, asymptotics of class groups and number fields;

Galois representations and (p-adic) automorphic forms.

UofT Mathematics Department's Equity Forum (website coming soon!)

UofTCensure - What did we achieve?

PDF
Video

Day of Refusal to Demand Cops off Campus Resources

Cops of Campus Resources - includes a resource section

Demands
Pledge

May 3rd Video Lecture for Educators
UofT-specific Learning Resources

#ScholarStrike Resources

#ScholarStrikeCanada - includes a schedule of teach-ins on September 9-10
#ScholarStrike - led by Dr. Anthea Butler and Dr. Kevin Gannon occurring on September 8-9

Teach-in Video Playlist - compilation of speeches, documentaries, and interviews related to policing in America.

ShutdownSTEM Resources

shutdownstem.com
Particles for Justice - led by Dr. Brian Nord & Dr. Chanda Prescod-Weinstein
Educational Material for Academics - for academic reading on STEM, Higher Education, and the BIPOC community
Symplectic Group Action - group toolbox used by math academia allies of BLM for learning and acting
Black Lives Matter Toronto - short videos featuring Sandy Hudson

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

Contact Info
.
Email: 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

Preprints

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
(submitted)

11. Geometry-of-numbers methods in the cusp
with Arul Shankar, Artane Siad, and Ashvin Swaminathan
(submitted)

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)

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

8. The mean number of 3-torsion elements in ray class groups of quadratic fields
(accepted, to appear in the Israel Journal of Mathematics)

Papers

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

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, and 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

Current 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*
Winter 2019	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