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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.

Monday, February 4, 2019

Monday, February 11, 2019

Monday, February 18, 2019

Monday, April 8, 2019

Monday, April 29, 2019

Monday, May 6, 2019