Logarithmic enumerative geometry

学生将在对数和热带枚举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学的界面，与数学弦理论的各个方面密切相关。工作将围绕几何的模空间的稳定映射和层的对数射影流形，在近年来取得了重大进展。第一个方向的研究可能涉及计算的等变周上同调环的对数映射空间，并将继续审查应用枚举几何问题的当代和经典的兴趣。

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.