Jake Levinson Assistant Professor Department of Mathematics Simon Fraser University e-mail: jake (underscore) levinson (at) sfu (dot) ca

I have moved! You can find me here.

Hello! I am an assistant professor in the Mathematics Department at Simon Fraser University. My research is in algebraic geometry and combinatorics.

Here is my CV.

Research

I am primarily interested in algebraic geometry and algebraic combinatorics. My current research involves moduli of stable curves, Schubert calculus, toric varieties and equivariant free resolutions. 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 doubled crystal.

I would love to talk to you about: GL_n representation theory and Schubert calculus, flags and Grassmannians, moduli spaces of stable curves, Hilbert schemes, homological algebra, and other "concrete" and combinatorial aspects of algebraic geometry, commutative algebra, and representation theory.

Teaching

Papers

(with Brooke Ullery and David Stapleton) Minimal degree fibrations in curves and the asymptotic degree of irrationality of divisors. Submitted (2023).
[arxiv]

(with Maria Gillespie and Sean T. Griffin) A proof of a conjecture of Monin and Rana on equations defining M_{0,n}. Submitted (2022).
[arxiv]

(with Maria Gillespie and Sean T. Griffin) Lazy tournaments and multidegrees of a projective embedding of M_{0,n}. Combinatorial Theory, to appear (2022).
[CT (temporary)] [arxiv]

(with Maria Gillespie and Sean T. Griffin) Degenerations and multiplicity-free formulas for products of psi and omega classes on M_{0,n}. Submitted (2022).
[arxiv]

(with Maria Gillespie and Sean T. Griffin) Tournaments and slide rules for products of psi and omega classes on M_{0,n} (extended abstract). Séminaire Lotharingien de Combinatoire (FPSAC 2022), 86B (2022), Art. 50, 12 pp.
[FPSAC]

(with Brooke Ullery) A Cayley-Bacharach theorem and plane configurations. Proceedings of the American Mathematical Society, 150 (2022), 4603-4618.
[PAMS] [arxiv]

(with Ben Adlam and Jeffrey Pennington) A random matrix perspective on mixtures of nonlinearities in single-layer neural networks. Proceedings of The 25th International Conference on Artificial Intelligence and Statistics (2022).
[NeurIPS] [arxiv]

(with Sean T. Griffin and Alexander Woo) Springer fibers and the Delta Conjecture at t=0. Submitted (2021).
[arxiv]

(with Sean T. Griffin and Alexander Woo) Springer fibers and the Delta Conjecture at t=0 (extended abstract). Séminaire Lotharingien de Combinatoire (FPSAC 2021), 85B (2021), Art. 76, 12 pp.
[FPSAC]

(with Kevin Purbhoo) A topological proof of the Shapiro-Shapiro conjecture. Inventiones Mathematicae, vol. 226 (2021), no. 2, 521--578.
[IM] [arXiv]

(with Carlos Esteves, Kefan Chen, Noah Snavely, Angjoo Kanazawa, Afshin Rostamizadeh and Ameesh Makadia) An Analysis of SVD for Deep Rotation Estimation. Advances in Neural Information Processing Systems 33 (NeurIPS 2020), 22554--22565.
[NeurIPS] [arxiv]

(with Kevin Purbhoo) Class groups of open Richardson varieties in the Grassmannian are trivial. Journal of Commutative Algebra 14(2), 267-275, (2022).
[JCA] [arXiv]

(with Maria Gillespie and Kevin Purbhoo) Schubert curves in the orthogonal Grassmannian. Discrete and Computational Geometry, to appear (2022).
[arXiv]

(with Maria Gillespie and Kevin Purbhoo) A crystal-like structure on shifted tableaux. Algebraic Combinatorics, vol. 3 (2020), no. 3, 693-725.
[AC] [arXiv]

(with Maria Gillespie) Axioms for shifted tableau crystals. Electronic Journal of Combinatorics, vol. 26 (2019), no. 2, #P2.2, 38 pp.
[EJC] [arXiv]

(with Nic Ford) Foundations of Boij-Söderberg theory for Grassmannians. Compositio Mathematica, vol. 154 (2018), no. 10, 2205-2238.
[CM] [arXiv] [Haverford slides]

(with Nic Ford and Steven Sam) Towards Boij-Söderberg theory for Grassmannians: the case of square matrices. Algebra and Number Theory, vol. 12 (2018), no. 2, 285-303.
[ANT] [arXiv]

(with Maria Gillespie and Kevin Purbhoo) Shifted tableau crystals (extended abstract). Séminaire Lotharingien de Combinatoire (FPSAC 2018), 80B (2018), Art. 71, 12 pp.
[FPSAC] [arxiv] [FPSAC slides]

(with Maria Gillespie) Monodromy and K-theory of Schubert curves via generalized jeu de taquin. Journal of Algebraic Combinatorics, vol. 45 (2017), no. 1, 191--243.
[JACO] [arXiv]

(with Maria Gillespie) Monodromy and K-theory of Schubert curves via generalized jeu de taquin (extended abstract). Discrete Mathematics and Theoretical Computer Science Proceedings (28th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2016), 551--562.
[FPSAC] [arxiv] [UW slides]

One-dimensional Schubert problems with respect to osculating flags. Canadian Journal of Mathematics, vol. 69 (2017), no. 1, 143--185.
[CJM] [arXiv]

(with Steven J. Miller) The n-level densities of low-lying zeros of quadratic Dirichlet L-functions. Acta Arithmetica, vol. 161 (2013), 145--182.
[AA] [arXiv]

(with Nick Arnosti, Rachel Karpman, Caitlin Leverson and Susan Loepp) Semilocal formal fibers of minimal prime ideal of excellent reduced local rings. Journal of Commutative Algebra, vol.4 (2012) no.1, 29--56.
[JCA]

Other writing

Review of "The BIG Jobs Guide: Business, Industry, and Government Careers for Mathematical Scientists, Statisticians, and Operations Researchers". Notices of the American Mathematical Society, May 2022.
[notices]

Expository writeups