Jake Levinson Jake Levinson
Assistant Professor
Department of Mathematics
Simon Fraser University

e-mail: jake (underscore) levinson (at) sfu (dot) ca


Hello! I am an assistant professor in the Mathematics Department at Simon Fraser University. My research is in algebraic geometry and combinatorics.

Here is my CV.

Research

I am primarily interested in algebraic geometry and algebraic combinatorics. My current research involves Schubert calculus, equivariant free resolutions and moduli of stable curves. For example, here is a combinatorial covering space called a 'Schubert curve', and some related Young tableaux. Here are some gln word crystals; and here is a doubled crystal.

I would love to talk to you about: GL_n representation theory and Schubert calculus, flags and Grassmannians, Hilbert schemes and related moduli problems (such as moduli of curves), homological algebra, and other "concrete" algebraic geometry, commutative algebra, and representation theory.

Teaching

Winter 2021: Math 440 Galois Theory
Fall 2020: Math 340 Intro to Abstract Algebra (rings and fields)

Papers

Class groups of open Richardson varieties in the Grassmannian are trivial, joint with K. Purbhoo. Preprint (2019).
[arXiv]

A topological proof of the Shapiro-Shapiro conjecture, joint with K. Purbhoo. Preprint (2019).
[arXiv]

A random matrix perspective on mixtures of nonlinearities in single-layer neural networks, joint with B. Adlam and J. Pennington. Submitted (2019).

Latent feature disentanglement for 3D meshes, joint with A. Makadia and A. Sud. Submitted (2019).
[arXiv]

Schubert curves in the orthogonal Grassmannian, joint with M. Gillespie and K. Purbhoo. Submitted (2019).
[arXiv]

Axioms for shifted tableau crystals, joint with M. Gillespie. Electronic Journal of Combinatorics (2019).
[EJC] [arXiv] [FPSAC abstract] [FPSAC slides]

A crystal-like structure on shifted tableaux, joint with M. Gillespie and K. Purbhoo. Algebraic Combinatorics, to appear (2019).
[arXiv]

Foundations of Boij-Söderberg Theory for Grassmannians, joint with Nic Ford. Compositio Mathematica (2018). [arXiv] [Haverford slides]

Towards Boij-Söderberg Theory for Grassmannians: the case of square matrices, joint with Nic Ford and Steven Sam. Algebra and Number Theory 12-2 (2018).
[arXiv]

K-theory and Monodromy of Schubert Curves via Generalized Jeu de Taquin, joint with M. Gillespie, Journal of Algebraic Combinatorics (2016).
[JACO] [arXiv] [FPSAC abstract] [UW slides]

One-dimensional Schubert problems with respect to osculating flags, Canadian Journal of Mathematics (2016).
[CJM] [arXiv]

n-Level Densities of Low-Lying Zeros of Quadratic Dirichlet L-functions, joint with Steven J. Miller, Acta Arithmetica 161 (2013), pp145-182.
[AA] [arXiv] and Mathematica notebooks for this paper: FourierIdentity.tar

Semi-Local Formal Fibers of Minimal Prime Ideals of Excellent Reduced Local Rings, joint with N. Arnosti, R. Karpman, C. Leverson, S. Loepp, Journal of Commutative Algebra, Vol. 4, No. 1, 2012.
[pdf]

Expository writeups

Special cosine values (2012): When is cos(2pi/m) algebraic of degree at most 4 over the rationals?
[pdf]

"Carrying the tens" and Ext (2016): The "carrying tens" rule for long-form addition is related to Ext!
[pdf]

For fun: some random domino tilings showcasing the Arctic Circle Phenomenon.

An introduction to Schubert Calculus (mini-course, 5 days), July 2015. notes here: Intro 1 1.5 2 3 4 5.
Translating between geometry and algebra (mini-course, 5 days), July 2015. (Joint with Rebecca RG).

Recent and upcoming talks

Algecom, UIUC (March 2020) [slides]
FRAGMENT Seminar, CSU (April 2020)
NU-UIC-UC Algebra Seminar (July 2020)
Monodromy in Algebraic Geometry Workshop, ICERM (August 2020)
VirtualCoDays20 (December 2020)

Background

I completed my Ph.D at Michigan in 2017, advised by David Speyer. Following that, I spent four months as an NSERC Postdoctoral Fellow at LaCIM (UQAM, Montreal), then was an Acting Assistant Professor at the University of Washington, Seattle from 2017-2020. During that time, I also spent one year as an AI Resident at Google Research in New York.

I was an undergraduate at Williams College with a BA in mathematics, and I spent Fall 2009 in Hungary at the Budapest Semesters in Mathematics program, which I highly recommend! I also did commutative algebra at SMALL with Susan Loepp in 2009, which was a great introduction to mathematical research. My undergraduate thesis was on L-functions and random matrices, advised by Steven J. Miller.

I am from Montreal, Quebec. I love bagels and occasionally poutine, et je parle français (mais je suis anglophone / English is my mother tongue).