Henry Liu

Research

Very broadly, my research interests lie at the intersection of algebraic geometry, representation theory, and mathematical physics. I like to study various moduli of sheaves, especially on surfaces or 3-folds (or 4-folds, on adventurous days), and their enumerative invariants and (quantum) symmetries.

Lately I've been thinking about vertex algebras.

Links to: my arXiv, my ORCID.

Papers and preprints

  1. The 3-fold K-theoretic DT/PT vertex correspondence holds
    with Nick Kuhn and Felix Thimm
    Preprint (2023) [arXiv:2311.15697] [slides]
  2. Semistable refined Vafa-Witten invariants
    Submitted (2023) [arXiv:2309.03673]
  3. The 4-fold Pandharipande-Thomas vertex
    Submitted (2023) [arXiv:2306.12923]
  4. Multiplicative vertex algebras and quantum loop algebras
    Submitted (2022) [arXiv:2210.04773]
  5. Equivariant K-theoretic enumerative invariants and wall-crossing formulae in abelian categories
    Preprint (2023) [arXiv:2207.13546]
    This paper is currently undergoing a mild revision/elaboration.
  6. A representation-theoretic approach to qq-characters
    SIGMA 18 (2022), 090 [arXiv:2203.07072] [Journal]
  7. Asymptotic representations of shifted quantum affine algebras from critical K-theory
    PhD. Thesis (2021), Columbia University [Academic Commons]
  8. Quasimaps and stable pairs
    Forum Math. Sigma 9 (2021), e32 [arXiv:2006.14695] [Journal]
  9. Self-duality in quantum K-theory
    Preprint (2019) [arXiv:1906.10824]
    I intend to revisit this project at some point in the future.
  10. No Laplacian Perfect State Transfer in Trees
    with Gabriel Coutinho
    SIAM J. Discrete Math., 29(4) (2015), 2179-2188 [arXiv:1408.2935] [Journal]
  11. Cardinality estimation using neural networks
    with Mingbin Xu, Ziting Yu, Vincent Corvinelli and Calisto Zuzarte
    CASCON 2015, 53-59 [Journal]
    A project from a past life.

Software

I have written and am maintaining some code (GitHub repository) for box-counting computations in SageMath. Here are some of the more useful objects that are implemented:

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