Logarithmic enumerative geometry

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The student will undertake research in the general area of logarithmic and tropical enumerative geometry. These areas lie at the interface of algebraic geometry and polyhedral combinatorics, and are closely connected to various aspects of mathematical string theory. The work will center around the geometry of the moduli space of stable maps and of sheaves on logarithmic projective manifolds, where significant progress has been made in recent years. The first direction of study is likely to concern the calculation of the equivariant Chow cohomology rings of logarithmic mapping spaces, and will proceed to examine applications to enumerative geometric questions of contemporary and classical interest.