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. Here are some gln word crystals; and here is a doubled crystal. TeachingMath 308I: Introduction to Matrix Algebra.Papers
Class groups of open Richardson varieties in the Grassmannian are trivial, joint with K. Purbhoo. Preprint (2019).
A topological proof of the Shapiro-Shapiro conjecture, joint with K. Purbhoo. Preprint (2019).
A random matrix perspective on mixtures of nonlinearities in single-layer neural networks, joint with B. Adlam and J. Pennington. Submitted (2019).
Latent feature disentanglement for 3D meshes, joint with A. Makadia and A. Sud. Submitted (2019).
Schubert curves in the orthogonal Grassmannian, joint with M. Gillespie and K. Purbhoo. Submitted (2019).
Axioms for shifted tableau crystals, joint with M. Gillespie. Electronic Journal of Combinatorics (2019).
A crystal-like structure on shifted tableaux, joint with M. Gillespie and K. Purbhoo. Algebraic Combinatorics, to appear (2019). Foundations of Boij-Söderberg Theory for Grassmannians, joint with Nic Ford. Compositio Mathematica (2018). [arXiv] [Haverford slides]
Towards Boij-Söderberg Theory for Grassmannians: the case of square matrices, joint with
Nic Ford and Steven Sam. Algebra and Number Theory 12-2 (2018).
K-theory and Monodromy of Schubert Curves via Generalized Jeu de
Taquin, joint with M. Gillespie, Journal of Algebraic Combinatorics (2016).
One-dimensional Schubert problems with respect to osculating
flags, Canadian Journal of Mathematics (2016).
n-Level Densities of Low-Lying Zeros of Quadratic Dirichlet L-functions, joint with Steven J. Miller, Acta Arithmetica
161 (2013), pp145-182. 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 writeupsSpecial 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. An introduction to Schubert Calculus (mini-course, 5 days), July 2015. notes here: Intro 1 1.5 2 3 4 5. Translating between geometry and algebra (mini-course, 5 days), July 2015. (Joint with Rebecca RG). Recent and upcoming talks
BackgroundI spent May-September 2017 as an NSERC Postdoctoral Fellow at LaCIM (UQAM, Montreal). Before that, I completed my Ph.D at Michigan in 2017, advised by David Speyer.I was an undergraduate at Williams College with a BA in mathematics, and I spent Fall 2009 in Hungary at the Budapest Semesters in Mathematics program, which I highly recommend! I also did commutative algebra at SMALL with Susan Loepp in 2009, which was a great introduction to mathematical research. (I also worked with Steven J. Miller on L-functions and random matrices, making me a proud member of the Miller Mafia). If you're a student thinking about applying to math grad schools, feel free to get in touch! I am Canadian. More specifically, I am from Montreal, Quebec. I love bagels and occasionally poutine, et je parle français (mais je suis anglophone / English is my mother tongue). |