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

East Hall 2852
530 Church Street
Ann Arbor, MI 48109-1043
e-mail: jakelev (at) umich (dot) edu


I am a fourth year Ph.D student working with David Speyer.

Research

I am primarily interested in algebraic geometry and algebraic combinatorics. My current research involves Schubert calculus and the moduli space of marked stable curves. For example, here is a combinatorial covering space I call a 'Schubert curve'. Here are some gln word crystals, and here is a link to my math blog.

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

One-dimensional Schubert problems with respect to osculating flags. Preprint.
[arXiv link]

n-Level Densities of Low-Lying Zeros of Quadratic Dirichlet L-functions, joint with Steven J. Miller, Acta Arithmetica 161 (2013), pp145-182.
[arXiv link] 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 link]

Teaching

Current:Past:
Fall 2015: TBA.
116 Calculus 2: W12 F12 F13 (co-coord) W14 F14
216 Differential Equations (TA): W13
115 Calculus 1: F11

Talks and Presentations

Invited

(Real) Schubert Calculus from marked points on P^1.
UW-Madison Algebraic Geometry Seminar, November 2015 (upcoming)
UIUC Algebraic Geometry Seminar, September 2015 (upcoming)
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.

Expository

Student Algebraic Geometry Seminar (UM):
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):
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.

Other:
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.

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.