Jake Levinson Jake Levinson
PhD Student
Department of Mathematics
University of Michigan

East Hall 2074
530 Church Street
Ann Arbor, MI 48109-1043
e-mail: jakelev (at) umich (dot) edu


I am a sixth year Ph.D student working with David Speyer. 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. And here are some gln word crystals.

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.

Prior to working in geometry, I wrote an undergraduate thesis with Steven J. Miller on L-functions and random matrices. (This makes me part of the Miller Mafia). I also did commutative algebra at SMALL with Susan Loepp in 2009; we constructed a class of strange singularities and studied them analytically-locally.

Papers

Foundations of Boij-Söderberg Theory for Grassmannians, joint with Nic Ford. Preprint.
[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] [FPSAC slides] [CAGE 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.

Teaching

Current:Past:
(none) 116 Calculus 2: W12 F12 F13 (co-coord) W14 F14
216 Differential Equations (TA): W13
115 Calculus 1: F11

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

Boij-Söderberg theory for Grassmannians
Fields Institute, Toronto, November 2016
Utah Commutative Algebra Seminar, December 2016
AMS-MAA Joint Math Meetings, January 2017
Berkeley CA&AG (Eisenbud) Seminar, January 2017
Washington Algebraic Geometry Seminar, January 2017

K-theory and monodromy of Schubert curves.
Minnesota Combinatorics Seminar, October 2016
Philadelphia CAGE Seminar, November 2016
SFSU Geometry and Topology Seminar, January 2017
Washington Combinatorics Seminar, January 2017

Syzygies and matrix varieties.
Haverford Math Colloquium, November 2016.

(Real) Schubert calculus from marked points on P^1.
York Algebraic Combinatorics Seminar, September 2016

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. If you're a Williams student thinking about applying to math grad schools, feel free to get in touch! I can't guarantee to be helpful, but I can guarantee to be more helpful than either of these guys.

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

Undergrad Thesis:

Download my undergraduate thesis and accompanying Mathematica notebooks: downloads page

Qual Solutions:

I wrote up my solutions to the May 2012 Analysis QR Exam, since there are currently no solutions to any analysis quals... that made it hard to study! Download here.