Math and biology

About me

I’m interested in genetic analysis of high-dimensional complex traits and in the genome’s physical conformation. While I was at Brown for my undergrad, I spent some time learning math, so I also care about certain topics there. In particular, I like hyperplane arrangements, moduli spaces, and their topology/combinatorics. These days, I think about:

• Genetically-informed representations of medical images
• Topological data analysis applied to single-cell genome conformation data
• Algebraic structures on various combinatorial objects related to threshold graphs
• Cohomology of configuration spaces on P^n, with collinearity constraints
• The (permutation?) S_n representations on the graded pieces of the cohomology of M_{0,n}-bar

I’m actively hoping to learn more about (i.e. please teach me about):

• Structural analysis of proteins
• Methods for time series analysis, especially comparing various time series
• Combinatorial decompositions of Springer fibers and Schubert varieties
• Brill-Noether theory

Papers

• Some algebraic aspects of threshold graphs (with Megan Chang-Lee and Melody Chan, in preparation)
  We computed the Frobenius characteristic of the S_n representation on labelled threshold graphs in two ways, identified a Hopf algebra structure on threshold graphs and interpreted the antipode graph-theoretically, gave evidence for the equivariant log-concavity of the Orlik-Solomon and Cordovil algebras of hyperplane arrangements, and studied persistence modules for filtrations of threshold graphs and shifted flag complexes.
• Wang, J., Jain, S., Chen, D. et al. Development and Evaluation of Novel Statistical Methods in Urine Biomarker-Based Hepatocellular Carcinoma Screening. Sci Rep 8, 3799 (2018). https://doi.org/10.1038/s41598-018-21922-9
  I worked with some extensions of random forest to develop a screening method for hepatocellular carcinoma.

Misc

• Find me on Goodreads, where I write increasingly long and incoherent book reviews! I read a lot of modern and contemporary Japanese literature as well as various other literary fiction.
• I’m a follower of Jesus Christ, who saw my sin and bore it for me. I love having conversations about faith and am always happy to talk with you about why I believe (and why I hope you will too).