Mathematical Sciences: Moduli Problems and Iterated Loop Spaces in Mathematical Physics

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Charles Boyer will continue his research into moduli problems which arise in mathematical physics. This is currently one of the most active areas of mathematics and has been shown to have profound consequences in mathematical physics, topology and geometry. The motivation for much of Boyer's work is the realization that many moduli problems in mathematics and mathematical physics are intimately related to the homotopy theory of iterated loop spaces. It is this observation that reveals the relationship between the topology of the moduli spaces and the differential topology of the underlying four dimensional manifold. Boyer's work is expected to shed further light on this relationship. It also holds promise of revealing deeper understanding of connections between algebraic topology and geometric non-linear partial differential equations.