Hebrew University topology and geometry seminar



December 31, 2014
1100-1235
Ross building, Seminar Room 63



Jonathan Rosenberg

University of Maryland

Duality for Elliptic Curve Orientifolds and Twisted KR-Theory




Abstract: An amazing discovery of physicists is that there are many seemingly quite different physical quantum field theories that lead to the same observable predictions.
Such theories are said to be related by dualities. A duality leads to interesting mathematical consequences; for example, certain K-theory groups on the two spacetime manifolds have to be isomorphic. Mirror symmetry of Calabi-Yau manifolds was also discovered this way. We will discuss the special case of elliptic curve orientifolds, complex) elliptic curves equipped with a holomorphic or anti-holomorphic involution. In this case, the relevant kind of K-theory is Atiyah's KR-theory, which we will define and explain, but certain additional twisting has to be taken into account.
It turns out that predictions from physics do match very nicely with calculations into topology. Some of this work is joint with Stefan Mendez-Diez and Chuck Doran.


Slides from the talk.