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 third year Ph.D student working with David Speyer.

Research

I am primarily interested in algebraic geometry and algebraic combinatorics. For example, 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. I also have a soft spot for (geometrically-motivated) commutative algebra.

I also like number theory, but my interest (and knowledge) is basic and mostly limited to the algebraic side (class field theory and Galois representation theory, arithmetic geometry). My undergraduate thesis (advised by Steven J. Miller) was in the theory of L-functions and random matrices. (This makes me part of the Miller Mafia).

In 2009, I worked in the commutative algebra group at SMALL with Susan Loepp, studying completions of certain (strange) local rings. Basically, we constructed a class of weird singularities, which we studied analytically-locally.

Preprints and Papers

n-Level Densities of Low-Lying Zeros of Quadratic Dirichlet L-functions, Jake Levinson and 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, N. Arnosti, R. Karpman, C. Leverson, J. Levinson, S. Loepp, Journal of Commutative Algebra, Vol. 4, No. 1, 2012.
[pdf link]

Teaching

Current: Past:
Winter 2014: 116 Calculus 2 Fall 2013: 116 Calculus 2 (co-coordinator)
Winter 2013: 216 Differential Equations
Fall 2012: 116 Calculus 2
Winter 2012: 116 Calculus 2
Fall 2011: 115 Calculus 1

Talks and Presentations

Schubert Problems from Marked Points on P^1, Student Algebraic Geometry Seminar (UM), March 2014.
Random Domino Tilings and the Arctic Circle Theorem, Student Combinatorics Seminar (UM), January 2014.
[small tiling], [large tiling], [elliptic tiling], [shuffling movie]
Genus of Curves and Brill-Noether theory, Student Algebraic Geometry Seminar (UM), September 2013.
Class Field Theory of P^1 over a Finite Field, Student Arithmetic Seminar (UM), April/May 2013.
Local Fields and Galois Representations, Student Arithmetic Seminar (UM), February 2013.
n-Level Densities of Zeros of Quadratic Dirichlet L-functions, Joint Math Meetings, January 2012; and YMC 2011, August 2011; and thesis defense at Williams College, May 2011.

Schedule:

Click here for my schedule.

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.