Kelly Wang

I am a second year phd student of Oscar Randal-Williams at the University of Cambridge.

I am interested in looking at homological stability via a homotopical lens, and anything broadly related.

Before this I was doing undergraduate and Part III at Cambridge.

Email: qw267 at cam dot ac dot uk

Office: E0.01

Publications and preprints

Periodic families in the homology of GL_n(F_2)

Kelly Wang

2026

abstract arXiv pdf

We construct infinite families of nonzero classes in H_d(GL_n(\F_2);\F_2) along lines of the form d =\frac23n + (constant), thereby showing that the known slope \frac23-stability for these homology groups are optimal. Using the new stability Hopf algebra perspective of Randal-Williams, our computations in addition recover the slope-\frac23 stability for \GL_n(\Z) with coefficients in \F_2, improve that for \Aut(F_n) to \frac23, and demonstrate that those slopes are optimal. Perhaps of independent interest, we also provide a manual for computing stability Hopf algebras over F_2.
@unpublished{periodic_families, title = {Periodic families in the homology of $GL_n(F_2)$}, author = {Wang, Kelly}, year = {2026}, }