Pentagon K3 surfaces

Location: 11th Floor Lecture Hall Speaker Flora Poon, National Center for Theoretical Sciences Abstract We will consider the configuration spaces of pentagons with fixed real side lengths modulo orientation preserving isometries. If we generalise the definition of pentagons by allowing their angles to be complex, such a configuration space is known to be a Hessian quartic K3 surface. With reference to Dolgachev and Keum's work, we will realise properties of Hessian quartic K3 surfaces, including elliptic fibrations and automorphisms, in terms of properties of pentagons. We will also explore the possibilities of computing relations in the automorphism group. This is joint work in progress with Harry Richman.