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 mysterious new crystal that Maria Gillespie and I are investigating. Papers
A crystal-like structure on shifted tableaux, joint with M. Gillespie and K. Purbhoo. Preprint.
Foundations of Boij-Söderberg Theory for Grassmannians, joint
with Nic Ford. Submitted.
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).
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. Teaching
I also taught two mini-courses in July 2014: An introduction to Schubert Calculus: 5-days, notes here: Intro 1 1.5 2 3 4 5. Translating between geometry and algebra: 5-days (taught jointly with Rebecca RG). Recent and upcoming talks
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 français (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. |