Will Dana's home page

I am a fifth-year PhD student in the Department of Mathematics at the University of Michigan, Ann Arbor.
I graduated in 2017 from the University of Washington, Seattle, with a B.S. in mathematics and a minor in music.

Contact info

Email: willdana at umich dot edu
Office: East Hall 3852

Research

I am broadly interested in combinatorics and representation theory. Specifically, I'm currently studying relationships between Coxeter groups, quiver representations, and representations of preprojective algebras. My advisor is David Speyer.
I've also looked at Brascamp-Lieb inequalities, integral inequalities associated to certain quiver representations, with Harm Derksen.
Some things I'd like to learn more about are tilting, geometric invariant theory, flag varieties, and representation stability. I also enjoy category-theoretic perspectives on things.

Writing

Teaching

UM

Fall 2017: Math 105.
Winter 2018: Math 115.
Fall 2018: Math 116.
Winter 2019: Math 116.
Fall 2021: Math 105.
(the latter third of) Winter 2022: Math 115.

UW

At the University of Washington, I was the TA for the second-year honors calculus sequence in 2015-2016 (Math 334, 335, 336) and 2016-2017 (Math 334, 335, 336).

Mathcamp

In summer 2019, I was a mentor at Canada/USA Mathcamp. I taught classes on complex projective space, ring theory, quiver representations, and determinants, as well as two- and one-day classes on random spanning trees and matroids.
Here are notes for my class on quiver representations.
Here are notes for my class on determinants.
Here is a note on why the groundskeeper's algorithm for generating uniformly random spanning trees works.
Here are notes on my one-day class on matroids.
Please let me know if you find typos.

UM grad student minicourses

In summer 2020, I ran a grad student minicourse on representations of finite-dimensional algebras, following Auslander, Reiten, and Smalø's Representation Theory of Artin Algebras. Here are the slides from the course.
In summer 2021, I ran a grad student minicourse on Ringel-Hall algebras, following Kirillov's Quiver Representations and Quiver Varieties.
Here are the slides from the course.

Miscellany