Mathematics Program Presents
Degenerations and Classification
Tuesday, October 4, 2022
RKC 111
5:00 pm – 6:30 pm EDT/GMT-4
5:00 pm – 6:30 pm EDT/GMT-4
Elana Kalashnikov, University of Waterloo
Algebraic geometry is the study of ‘shapes’ cut out by polynomial equations. One of the major open problems facing mathematicians today is how to classify these shapes. More complicated shapes can be broken into basic building blocks - so to classify all varieties it suffices to classify the basic building blocks. In this talk, we’ll explain how insights in string theory have given mathematicians a promising way of classifying the building blocks using Mirror Symmetry. The key idea is that each building block should correspond to certain decorated polytopes. Given a building block, the question is then how to produce such a polytope: this is done by degenerating the equations cutting out the shape of the building block. We’ll discuss what’s known about this approach, and what’s left to do, along with explicit examples.For more information, call 845-758-6822, or e-mail [email protected].
Time: 5:00 pm – 6:30 pm EDT/GMT-4
Location: RKC 111