# Will Dana's home page

I am a third-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 representation theory and its overlaps with combinatorics and algebraic geometry. I am currently studying quiver representations and Coxeter groups with 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 flag varieties, geometric invariant theory, and representation stability. More casually, I also enjoy category-theoretic perspectives on things.
## Writing

- Jekel, David, Avi Levy, Will Dana, Austin Stromme, Collin Litterell. "Algebraic Properties of Generalized Graph Laplacians: Resistor Networks, Critical Groups, and Homological Algebra." SIAM J. Discrete Math., 32(2), 1040--1110, 2018. Preprint: arXiv:1604.07075.
- Dana, Will. "Seeing Galois Theory on Riemann Surfaces with Dessins d'Enfants." 2017. My senior thesis, an exposition on dessins d'enfants. Written under the guidance of Professor Jim Morrow.
- With David Jekel: A note on critical groups of graphs with dihedral symmetry.
- See also "Teaching - Other" below.

## Teaching

### UM

Fall 2017: Math 105.

Winter 2018: Math 115.

Fall 2018: Math 116.

Winter 2019: Math 116.
### 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).
### Other

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.
## Miscellany

- This semester, Alana Huszar and I are organizing the Student Combinatorics Seminar. Come by 3096 East Hall at 3 PM on Mondays, or ask one of us for more information!
- Outside of math, I enjoy puzzles and games, music (in particular electronic music), and baking.
- For non-math content, see my personal webpage.
- I was interviewed for this article about the Putnam exam at UW.