I am a sixth 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, 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 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 Lfunctions 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 analyticallylocally.
Papers
Towards BoijSöderberg Theory for Grassmannians: the case of square matrices, joint with
Nic Ford and Steven Sam. Preprint.
[arXiv]
Ktheory and Monodromy of Schubert Curves via Generalized Jeu de
Taquin, joint with M. Gillespie, Journal of Algebraic Combinatorics,
to appear.
[arXiv] [FPSAC
abstract] [FPSAC slides]
Onedimensional Schubert problems with respect to osculating
flags, Canadian Journal of Mathematics (2016).
[CJM] [arXiv]
nLevel Densities of LowLying Zeros of Quadratic Dirichlet Lfunctions, joint with Steven J. Miller, Acta Arithmetica
161 (2013), pp145182.
[arXiv] and
Mathematica
notebooks
for this paper: FourierIdentity.tar
SemiLocal 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]
Expository writeups
Special cosine values (2012): when is cos(2pi/m)
algebraic of degree at most 4 over the rationals?
[pdf link]
"Carrying the tens" and Ext (2016): the "carrying tens" rule
for longform addition is related to Ext!
[pdf link]
Teaching
Current:  Past: 
(none)

116 Calculus 2: W12 F12 F13 (cocoord) W14
F14
216 Differential Equations (TA): W13
115 Calculus 1: F11

Talks and Presentations
Research

Ktheory and monodromy of Schubert curves.
Philadelphia CAGE Seminar, November 2016 (upcoming)
FPSAC 2016, Vancouver, July 2016
Berkeley Combinatorics Seminar, April 2016
LaCIM, Montreal, April 2016
Michigan Combinatorics Seminar, January 2016
Joint Math Meetings, Seattle, January 2016

(Real) Schubert calculus from marked points on P^1.
Central Michigan University Algebra Seminar, March 2016
UWMadison Algebraic Geometry Seminar, November 2015
Toronto Geometric Representation Theory Seminar, November 2015
UIUC Algebraic Geometry Seminar, September 2015
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

nLevel densities of zeros of quadratic Dirichlet
Lfunctions.
Joint Math Meetings, January 2012
YMC 2011, August 2011
Honors thesis defense, Williams College, May 2011.

Expository
What is Schubert calculus?
FrankFest, Williams College, February 2016.
Student Algebraic Geometry Seminar (UM):
A Calculus for the Moduli Space of Curves, April 2016.
BoijSöderberg Theory in Geometry, November 2015.
Deformation to the normal cone, October 2014.
Schubert problems from marked points on P^1, March 2014.
Genus of curves and BrillNoether theory, September 2013.
Student Combinatorics Seminar (UM):
Monodromy of Schubert curves, October 2015.
Dual equivalence of tableaux, November 2014.
Schubert problems from marked genuszero 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: 5day minicourse, July
2014. (Notes here: Intro
1
1.5
2
3
4
5.)
Translating between geometry and algebra: 5day 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 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.

