# Sian Fryer

## sianfryer@math.ucsb.edu

### Pronouns: they/them

My main research interest is in noncommutative algebra, and in particular quantized coordinate rings / quantum algebras and their semi-classical limits. At the moment I'm mostly interested in H-primes in quantum matrices, and total non-negativity in real matrices and the Grassmannian.

You can find my PhD thesis here. If that's too long a read, you can see what the critics think here.

For a shorter introduction to my work on division rings, I suggest you try this poster; it is aimed at interested non-mathematicians and comes with a dramatic fire backdrop.

#### Papers and preprints

- (with S. Agarwala) An algorithm to construct the Le diagram associated to a Grassmann necklace (to appear in Glasg. Math. J.) arXiv
- (with S. Agarwala) A study in [Nonnnegative Real Grassmannians]: from the geometric case book of Wilson loop diagrams and SYM N = 4. (submitted, 2018) arXiv
- (with T. Kanstrup, E. Kirkman, A. Shepler, S. Witherspoon) Color Lie Rings and PBW Deformations of Skew Group Algebras (to appear in J. Alg) arXiv
- (with M. Yakimov) Separating Ore Sets for Prime Ideals of Quantum Algebras (Bull. Lond. Math. Soc. 49, 2017) arXiv
- (with K. Casteels) From Grassmann necklaces to restricted permutations and back again (Algebr. Represent. Theory 20, 2017) arXiv
- The Prime Spectrum of Quantum SL3 and the Poisson-prime Spectrum of its Semi-classical Limit (Trans. London Math. Soc. 4, 2017) arXiv
- The q-Division Ring and its Fixed Rings (J. Alg 204, 2014) arXiv