# Sian (Zee) Fryer

## fryer.zee@gmail.com

### 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 nonnegativity in real matrices and the real Grassmannian.

- You can find my academic CV here.
- Here is my Github, including Python code for manipulating positroids and Wilson loop diagrams
- 3B spring 2019 students: grade calculator is here.

#### For interested non-mathematicians

Here are some math outreach things I've created or been involved in; they're all aimed at mathematically-inclined people but don't require much specialist knowledge. Some of them even relate to my research!

- Poster explaining my PhD work on division rings. This reached the final of the STEM for Britain poster competition in 2015.
- Matt Parker's Domino computer

#### For mathematicians

The following documents go into more detail about my research, and are listed in roughly increasing order of specialisation.

- Research proposal on H-primes, totally nonnegative matrices, and applications to physics (2017, aimed at general mathematicians).
- Research statement (2015, aimed at algebraists).
- PhD thesis (2014, aimed at noncommutative algebraists).

#### Papers and preprints

- (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 1803.00958
- (with S. Agarwala) An algorithm to construct the Le diagram associated to a Grassmann necklace (to appear in Glasg. Math. J.) arXiv 1803.01726
- (with T. Kanstrup, E. Kirkman, A. Shepler, S. Witherspoon) Color Lie Rings and PBW Deformations of Skew Group Algebras (J. Algebra 518 (2019), 211-236) arXiv 1801.08855
- (with M. Yakimov) Separating Ore Sets for Prime Ideals of Quantum Algebras (Bull. Lond. Math. Soc. 49, 2017) arXiv 1602.05052
- (with K. Casteels) From Grassmann necklaces to restricted permutations and back again (Algebr. Represent. Theory 20, 2017) arXiv 1511.06664
- The Prime Spectrum of Quantum SL3 and the Poisson-prime Spectrum of its Semi-classical Limit (Trans. London Math. Soc. 4, 2017) arXiv 1505.06627
- The q-Division Ring and its Fixed Rings (J. Alg 204, 2014) arXiv 1310.5071