The ACO Seminar (2026–2027)

Say you have the Cayley graph G of an infinite group. Wouldn't it be nice if, for every R, there was a finite graph that looked like G in the R-neighborhood of every vertex? Failing that, wouldn't it be nice if this held for a 1-o(1) fraction of vertices? That's what it means for G to be sofic. Well, it's not always meant to be; per OpenAI (and using tools by Gábor Kun and Andreas Thom), there exists a non-sofic group. I'll try to tell you about it; it's about 90% spectral graph theory.