Seminar

K-theory of toric varieties

Many geometric invariants of a normal toric variety X can be described in terms of its associated polyhedral fan F. Fulton and Sturmfels described the Chow ring of a complete toric variety using Minkowski weights, which are a ring of integer-valued functions on F satisfying a balancing condition. These weights have appeared in many contexts since their introduction, including in tropical geometry where they are central to tropical intersection theory.

The functions they don't tell you about in calculus

The functions we use in a calculus class are typically very well behaved.  So much so that we get used to not checking hypotheses before applying a theorem.   For instance, when using Taylor's Theorem, when was the last time you had to check that a function was $n$-times differentiable?  We usually work with the likes of $e^x$, $\cos x$, and $\sin x$, which can be differentiated over and over without ever stopping.  In fact, without googling, could you give an example of a function that can \textit{only} be differentiated \textbf{twice} at a point?