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 just moved to Seattle to join UW as an acting assistant professor (i.e., a postdoc). Earlier this summer I was in Montreal as an NSERC Postdoctoral Fellow at LaCIM. Before that, I did my Ph.D at Michigan, advised by David Speyer.

Here is my CV.

Teaching

Autumn 2017: Math 308, Matrix Algebra.

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 mysterious new crystal that Maria Gillespie and I are investigating.

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 and commutative algebra.

Papers

A crystal-like structure on shifted tableaux, joint with M. Gillespie and K. Purbhoo. Preprint.
[arXiv]

Foundations of Boij-Söderberg Theory for Grassmannians, joint with Nic Ford. Submitted.
[arXiv] [Haverford slides]

Towards Boij-Söderberg Theory for Grassmannians: the case of square matrices, joint with Nic Ford and Steven Sam. Submitted.
[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.

I also taught two mini-courses in July 2014:

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

Recent and upcoming talks

Crystal structures on shifted tableaux [slides]
AMS Sectional Meeting, Hunter College NY, May 2017

Boij-Söderberg theory for Grassmannians
UC Davis Algebra and Discrete Math Seminar, May 2017
Séminaire du LaCIM, July 2017

Personal:

I graduated from Williams College with a BA in mathematics, and 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).