EVENT DETAILS AND ABSTRACT

Title: Super geometry and the foundations of perturbative string theory
Speaker: Ron Donagi
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Brief Description:
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Abstract:

Supergeometry studies two kinds of objects. A super object is an object equipped with an algebra of functions that is (Z/2)-graded commutative. Examples: supermanifolds, superschemes, super Lie groups, super Lie algebras. A supersymmetric object, on the other hand, has a much tighter structure involving the action of a supergroup that mixes the even and odd directions. Roughly, the odd directions look like spinors over the even directions. The smallest example is a super Riemann surface: a supersymmetric space with 1 even and 1 odd, spinorial direction. Their theory is very rich. In particular, their moduli spaces furnish very interesting and non trivial examples of supermanifolds (or better, superstacks). In particular, they are nn-split, meaning they cannot be reconstructed by elementary menas from nn-super data. Both these 'super moduli spaces' and their Deligne-Mumford compactifications play crucial roles in the foundations of perturbative superstring theory. I will explain and illustrate these basic notions, and if time allows might mention some related developments such as super toric varieties, super log structures and super Calabi-Yaus.