What about Giles Gardam's construction of non-trivial units in the mod-2 group algebra of a torsion-free group https://arxiv.org/abs/2102.11818, which solved an 80-year old conjecture, and Alan Murray's extension of Giles Gardam's work to the mod-$p$ group algebra of the same group for odd primes https://arxiv.org/abs/2106.02147? I'm not sure which category to put it in. There is an interview with Gardam in which he says that the computing he did only required his laptop, but that it was comforting to know that he could have done more with a bigger computer if necessary.