### About Me

I'm a postdoctoral researcher at the Center for Quantum Mathematics and Physics at UC Davis. I work on problems in representation theory, geometry, and combinatorics that are informed by theoretical physics, and am supported by NSF grant DMS-1801969.

### Research

Here is a list of my papers and preprints:

- Kasteleyn operators from mirror symmetry, with David Treumann and Eric Zaslow. (arXiv) (Selecta Math.)
- Cluster theory of the coherent Satake category, with Sabin Cautis. (arXiv) (J. Amer. Math. Soc.)
- Affine cluster monomials are generalized minors, with Dylan Rupel and Salvatore Stella. (arXiv) (Compos. Math.)
- On generalized minors and quiver representations, with Dylan Rupel and Salvatore Stella. (arXiv) (Int. Math. Res. Not.)
- On the combinatorics of exact Lagrangian surfaces, with Vivek Shende and David Treumann. (arXiv)
- Cluster varieties from Legendrian knots, with Vivek Shende, David Treumann, and Eric Zaslow. (arXiv) (Duke Math. J.)
- The greedy basis equals the theta basis, with Man-Wai Cheung, Mark Gross, Greg Muller, Gregg Musiker, Dylan Rupel, Salvatore Stella. (arXiv) (J. Combin. Theory Ser. A)
- Toda systems, cluster characters, and spectral networks. (arXiv) (Comm. Math. Phys.)
- Q-systems, factorization dynamics, and the twist automorphism. (arXiv) (Int. Math. Res. Not.)
- Cluster ensembles and Kac-Moody groups. (arXiv) (Adv. Math.)
- Double Bruhat cells in Kac-Moody groups and integrable systems. (arXiv) (Lett. Math. Phys.)

### Teaching

I am not currently teaching.

### Other Stuff

I was previously supported by NSF Postdoctoral Research Fellowship DMS-1502845 at the University of Texas at Austin.

I was an organizer of the 2016 Texas Algebraic Geometry Symposium, which was held April 2-3, 2016.

I like playing music, and as an undergraduate I studied classical guitar at the UT Austin School of Music.

I also work on machine learning and perception algorithms for self-driving cars as a research consultant for Helm.ai.

You can find more detailed biographical information in my CV.

### Contact Me

UC Davis

Department of Mathematics

1 Shields Ave

Davis, CA 95616

hwilliams@math.ucdavis.edu