I will introduce a program (started in https://arxiv.org/abs/1908.02162) of studying moduli stacks of varieties using ideas from (ancient) algebraic topology. In dimension zero, this amounts to the study of the Hilbert scheme of local complete intersections, while in negative (virtual) dimensions this amounts to the study of the moduli of derived thickenings of points. Time permitting, I will report on joint work in progress with Ryomei Iwasa in positive dimensions.