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:

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

Galois representations and (p-adic) automorphic forms.

#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

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)
(submitted)

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

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, 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 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