Logarithmic enumerative geometry

学生将在对数和热带计数几何的一般领域进行研究。这些领域位于代数几何和多面体组合数学的交界处，与数学弦理论的各个方面密切相关。这项工作将围绕稳定映射的模空间和对数射影流形上的层的几何展开，近年来在这方面已经取得了重大进展。第一个研究方向可能涉及对数映射空间的等变Chow上同调环的计算，并将继续研究其在当代和古典感兴趣的计数几何问题中的应用。

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.