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Thumbnail for The moments of this distribution are the cogrowth sequence of the lamplighter group

The moments of this distribution are the cogrowth sequence of the lamplighter group

September 06, 2025

The lamplighter group $L$ is well-studied in geometric group theory and related fields. This distribution came up in my study of random matrices associated to graphs; its moments are given exactly by the cogrowth sequence of $L$. I prove this and make some fun visualizations.

Thumbnail for The Class Field Tower Problem and Golod-Shafarevich Groups

The Class Field Tower Problem and Golod-Shafarevich Groups

August 18, 2025

This post is a summary of a writing project I did for a special topics course taken at the University of Washington with Dr. Be'eri Greenfeld. It's a bit of a longer, technical read.