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## January 23 | 2:00 pm - 3:00 pm EST

Even though the field with one element, $\mathbb{F}_1$, is a meaningless concept, shadows of it have been apparent in multiple categorical analogies. More immediately, one can generalize multiple constructions from algebraic geometry over $\mathbb{F}_{p^n}$ to general commutative monoids, which behave like rings over this elusive $\mathbb{F}_1$. In this talk we define, via this analogy, schemes over $\mathbb{F}_1$, and consider zeta functions over $\mathbb{F}_1$ varieties. These results are taken from arXiv:math/0404185.