Department of

December 2018 January 2019February 2019Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su MoTuWe Th Fr Sa 1 1 2 3 4 5 1 2 2 3 4 5 6 7 8 6 7 8 9 10 11 12 3 4 5 6 7 8 9 9 10 11 12 13 14 15 13 14 15 16 17 18 19 10 11 12 13 14 15 16 16 17 18 19 20 21 22 20 21 22 23 24 25 26 17 181920 21 22 23 23 24 25 26 27 28 29 27 28 29 30 31 24 25 26 27 28 30 31

Monday, January 28, 2019

**Abstract:** A circle action on a manifold can be thought of as a periodic flow on a manifold (periodic dynamical system), or roughly a rotation of a manifold. During this talk, we consider circle actions on almost complex manifolds, which are more general than symplectic manifolds. We discuss classification of a circle action on a compact almost complex manifold $M$, when the number $k$ of fixed points is small. If $k=1$, $M$ is a point. If $k=2$, $M$ resembles $S^2$ or $S^6$. If $k=3$, $M$ resembles $\mathbb{CP}^2$. We also discuss when $k=4$ and $\dim M \leq 6$. Techniques include equivariant cohomology and index theory.