Title: What polytopes tell us about toric varieties

Date: 03/28/2017

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

Polytopes are among the oldest mathematical objects that have been studied. Often, people want to find their volumes, identify triangulations, and describe their lattice points, and more. But why bother doing this? From a combinatorial perspective, the data often answer counting questions that one might have. However, there is much more depth from an algebro-geometric standpoint: this information is often useful for learning about certain toric varieties.
In the first of these talks, I will give the background needed to understand what a normal projective toric variety is and how to model them using polytopes. In the second talk, I will define several properties that an algebraic geometer may want to know about a toric variety, and explain how to detect these properties from a purely polytopal perspective.