### About Me

I'm a mathematician. I'm an NSF Postdoctoral Fellow and Geometry RTG Instructor at the University of Texas at Austin. I think about problems in representation theory, geometry, and combinatorics that are informed by mathematical physics.

### Research

Here is a list of my papers and preprints:

- Cluster theory of the coherent Satake category, with Sabin Cautis. (in preparation)
- Homological mirror symmetry and the Goncharov-Kenyon system, with David Treumann and Eric Zaslow. (in preparation)
- On generalized minors and quiver representations, with Dyland Rupel and Salvatore Stella. (arXiv)
- 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) (updated version)
- 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

Semester | Course | Time |
---|---|---|

Spring 2015 | M408K Differential Calculus | TTh 11:00 - 12:30 |

Fall 2014 | M408D Sequences, Series, and Multivariable Calculus | TTh 9:30-11:00 |

### Other Stuff

I am supported by NSF Postdoctoral Research Fellowship DMS-1502845 with sponsoring scientist Andrew Neitzke.

You can find more detailed biographical information in my CV.

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

### Contact Me

The University of Texas at Austin

Department of Mathematics, RLM 10.132

2515 Speedway Stop C1200

Austin, Texas 78712-1202

hwilliams@math.utexas.edu