Quantum Steenrod operations in non-monotone symplectic manifolds.

Seidel最近在单调辛流形的量子上同调上引入了量子Steenrod运算。阿曼达将使用Pardon的虚拟基本周期框架，在一般情况下(即非单调情况)定义这些类似物，她在硕士论文期间已经利用该框架获得了技术专长。然后，她可以研究许多性质和应用；例如，量子Steenrod运算如何与其他代数运算相互作用；动力学应用；以及哈密顿或拉格朗日Floer上同调的类似物。

Seidel recently introduced quantum Steenrod operations on the quantum cohomology of monotone symplectic manifolds. Amanda will work on defining analogues of these in the general (i.e. non-monotone case), using Pardon's framework for virtual fundamental cycles, with which she has already acquired technical expertise during her masters' thesis. There are a number of properties and applications she can then study; for instance, how quantum Steenrod operations interact with other algebraic operations; dynamical applications; and analogues for Hamiltonian or Lagrangian Floer cohomology.