Jake Levinson Jake Levinson
Acting Assistant Professor
Department of Mathematics
Padelford C-432
University of Washington

e-mail: jlev (at) uw (dot) edu


Hello! I am an acting assistant professor (i.e., a postdoc) in the Mathematics Department at UW. 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

Math 308I: Introduction to Matrix Algebra.

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

Algebraic Geometry Seminar, Harvard University (March 2019)
LaCIM, UQAM (July 2019)
AMS Sectional Meeting, Madison, WI (September 2019)
UW-PIMS Math Colloquium, UW-Seattle (October 2019) [slides]
Combinatorics Seminar, University of Michigan (October 2019)
Algebraic Geometry Seminar, UCSD (November 2019)
Colloquium, Simon Fraser University (November 2019) [slides]

Background

I spent May-September 2017 as an NSERC Postdoctoral Fellow at LaCIM (UQAM, Montreal). Before that, I completed my Ph.D at Michigan in 2017, advised by David Speyer.

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. (I also worked with Steven J. Miller on L-functions and random matrices, making me a proud member of the Miller Mafia).

If you're a student thinking about applying to math grad schools, feel free to get in touch!

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