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.


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.


Foundations of Boijd-Söderberg Theory for Grassmannians, joint with Nic Ford. Preprint.

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

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]

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.

Expository writeups

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

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


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

Talks and Presentations


K-theory and monodromy of Schubert curves.
Philadelphia CAGE Seminar, November 2016 (upcoming)
FPSAC 2016, Vancouver, July 2016
Berkeley Combinatorics Seminar, April 2016
LaCIM, Montreal, April 2016
Michigan Combinatorics Seminar, January 2016
Joint Math Meetings, Seattle, January 2016

(Real) Schubert calculus from marked points on P^1.
Central Michigan University Algebra Seminar, March 2016
UW-Madison Algebraic Geometry Seminar, November 2015
Toronto Geometric Representation Theory Seminar, November 2015
UIUC Algebraic Geometry Seminar, September 2015
MSU Algebra Seminar, April 2015
Texas A&M Geometry Seminar, March 2015
Berkeley Combinatorics Seminar, February 2015

Limit linear series and real Schubert calculus.
UIC Midwest Algebraic Geometry Graduate Conference, April 2015

n-Level densities of zeros of quadratic Dirichlet L-functions.
Joint Math Meetings, January 2012
YMC 2011, August 2011
Honors thesis defense, Williams College, May 2011.


What is Schubert calculus?
FrankFest, Williams College, February 2016.

Student Algebraic Geometry Seminar (UM):
A Calculus for the Moduli Space of Curves, April 2016.
Boij-Söderberg Theory in Geometry, November 2015.
Deformation to the normal cone, October 2014.
Schubert problems from marked points on P^1, March 2014.
Genus of curves and Brill-Noether theory, September 2013.

Student Combinatorics Seminar (UM):
Monodromy of Schubert curves, October 2015.
Dual equivalence of tableaux, November 2014.
Schubert problems from marked genus-zero stable curves, April 2014.
Random domino tilings and the Arctic Circle Theorem, January 2014.
[small tiling], [large tiling], [elliptic tiling], [shuffling movie]

Student Arithmetic Seminar (UM):
Class Field Theory of P^1 over a finite field, April/May 2013.
Local fields and Galois representations, February 2013.

An introduction to Schubert Calculus: 5-day mini-course, July 2014. (Notes here: Intro 1 1.5 2 3 4 5.)
Translating between geometry and algebra: 5-day mini course (taught jointly with Rebecca RG), July 2014.


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.