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Super Math

Ron Donagi, UPenn

Location:  HILL 705
Date & time: Friday, 27 October 2017 at 4:00PM - 5:00PM

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). 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.


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