PhD July 2010, University of Minnesota

BS 2003, California Institute of Technology

I am an assistant professor at the University of Minnesota working primarily with MCFAM, the Minnesota Center for Financial and Actuarial Mathematics. In 2013 I was at Cornell University, Ithaca, New York, to take advantage of the wonderful faculty and their cool mathematics, while Fall 2012 I was a Postdoctoral Research Fellow at the Mathematical Sciences Research Institute in Berkeley, California. In 2010-2012, I was a visiting assistant professor at St. Olaf College.

Coloring Book and math outside of academia

If you're interested in Math with Crayons -- Coloring Patterns from Modern Mathematics, you can buy it online. It's a coloring book of Penrose tilings, totally symmetric self-complementary plane partitions, fully packed loops, domino tilings of Aztec diamonds, and Postnikov diagrams! No equations, all fun patterns. If someone wanted to make it a required text for a college class somewhere in the state of Minnesota, that would eliminate all sales tax requirements -- send me a scan of your syllabus if you do this!

A few years ago I also wrote EarthCalculus, a book of worksheets and resources for instructors who want to incorporate problems involving nature into calculus classes. It's a fully digital book right now so that you can print out worksheets and have their solutions.


Graduate work with Prof. Ionut Ciocan-Fontanine. My thesis work: algebraic geometry -> Gromov-Witten theory -> using localization as a computational tool -> focusing on the abelian/nonabelian correspondence and establishing the K-theoretic J-functions for flags in type A. Now I'm focusing on equivariant Gromov-Witten invariants of Grassmannians (see in particular my papers with Elizabeth Milicevic and Anna Bertiger) and slowly working on understanding K-theoretic Gromov-Witten invariants more thoroughly. I am interested in the geometry and the combinatorics of these invariants, and emerging connections with cluster algebras.

If you want to work with me on research in financial mathematics or do a senior project with me, I am currently looking at cryptocurrencies, nature & math (including weather derivatives, catastrophe bonds, and commodities influenced by weather), and topological methods in finance, particularly in stress testing. If you want to do a senior project in algebraic geometry (pure or applied) feel free to talk with me about that as well.

I will also be working with students this year (2017-18) on programming for stress testing applications. It will primarily be in Python. Maybe you could make a senior undergraduate project out of this -- not sure.


This year (2017-2018) I will be teaching FM 5001 and 5002, Preparation for Financial Mathematics. This course covers linear algebra, multivariable calculus, probability, and statistics.

If you are a student, you will get access to our private Canvas site when you're enrolled. If you want to get a head start, review your calculus. Next step: consider looking in on Kjell Konis' Coursera course Mathematical Methods for Quantitative Finance. On the probability side, read the fun parts of the first six chapters of "Understanding Probability" by Henk Tijms, 3rd edition. It will be a required text for the course.

Click here for some more probability and financial math resources.

Old curriculum Vitae


If you have comments or notice errors, please email me!

Equivariant Quantum Cohomology of the Grassmannian via the Rim Hook Rule, submitted.

An equivariant rim hook rule for quantum cohomology of Grassmannians is the FPSAC take on the previous article, published in DMTCS Proceedings.

A combinatorial case of the abelian-nonabelian correspondence, arXiv, or the published version here.

K-theoretic J-functions of type A flag varieties. Published in International Mathematics Research Notices here.

Interesting things

Pictures from Oberwolfach.

How to Do What You Love, by Paul Graham. If you are studying mathematics, you should be in class because (a) you know you need it for something that you enjoy/are interested in, or (b) because you enjoy the math itself. If neither of these are true, why do it? And if one of the above is true, why not put in your best effort while you're in class? Putting in half an effort is a waste of your time.

Also check out the rest of Paul Graham's essays. How can you resist titles like, "Good and Bad Procrastination," and "Why Nerds are Unpopular?"

Paul Garrett's page, useful for that little intro to tex, some clues on modular forms, a certain point of view on universal mapping properties...

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The views and opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota.