Algebraic structures in topological field theory

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In quantum field theory, backgrounds with boundary are equivalent to their double, thought of as an oriented manifold with an orientation reversing involution (orientifold). For example, studying two-dimensional topological field theory in this way, one obtains a powerful approach to open/closed topological field theory. In this project, we will study the role of Z/2-equivariant homotopy and Z/2-equivariant Beilinson-Deligne/Cheeger-Simons cohomology in the formulation of topological field theories on manifolds with boundary, as well as in supergravity.Topological field theories arise in many places in theoretical physics and mathematics (and indeed in the theory of quantum computers). We are interested in understanding better the role of boundaries in the topological field theories that occur in supergravity theory, an important extension of Einstein's theory of General Relativity. Ultimately, boundaries in supergravity are related to problems in cosmology, including the many-worlds interpretation of quantum theory.