# Henry Liu

## Research

Most of the following publications and preprints are also listed on arXiv. Any comments, corrections or suggestions would be greatly appreciated.

1. (2020) Quasimaps and stable pairs, preprint.
2. (2019) Self-duality in quantum K-theory, preprint.
3. (2015) No Laplacian Perfect State Transfer in Trees, SIAM J. Discrete Math., 29(4), 2179-2188.
4. (2015, in a past life) Cardinality estimation using neural networks, CASCON 2015, 53-59.

Sometimes I also like to write notes while I am acquainting myself with new objects and concepts. Undoubtedly these notes contain no novel material, but here they are in the hopes that they will be helpful to other people in the future.

### Software

Since 2018, I have been writing code in SageMath for box-counting computations, available here as a GitHub repository. Here are some of the more useful objects that are implemented.

• 3d partitions (with legs)
• Fully equivariant 3-leg DT and PT vertices in cohomology and K-theory (checked to be equal, after normalization, up to legs of size 4 and 6 extra boxes)
• The elliptic Hall algebra $$U_q(\hat{\hat{\mathfrak{gl}}}_1)$$ and its Fock representation on symmetric polynomials.

If you are also counting boxes and would like a new feature implemented, feel free to let me know.