### Geometry of rational curves on some varieties with a Lie group action

Algebra and Geometry Seminar

6th February 2019, 2:30 pm – 3:30 pm

Howard House, 4th Floor Seminar Room

In this talk, I will describe a family of algebraic varieties with actions of Lie groups which are closely related to homogeneous spaces (which for instance include projective spaces, quadrics, Grassmannians). After describing the geometry and the orbit structure of these varieties, I will explain how to understand rational curves on these varieties, as well as an algebraic structure encoding the intersection theory of these curves, called the quantum cohomology ring. This is joint work with R. Gonzales, N. Perrin, and A. Samokhin.

*Biography:*

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