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# All ALH* Gravitational Instantons as the Moduli Space of Doubly Periodic Monopoles

### Mathematical Physics and Probability Seminar

All ALH* Gravitational Instantons as the Moduli Space of Doubly Periodic Monopoles
Series: Mathematical Physics and Probability Seminar
Location: MATH 402
Presenter: Thomas Harris, University of Arizona

Gravitational Instantons are Riemannian solutions of the Einstein Field Equations from General Relativity. ALH* Gravitational Instantons are ones such that the asymptotic volume growth of balls of radius R approaches R^{4/3}. Thanks to recent work in 2021, all ALH* gravitational instantons were classified by Hein, Sun, Viaclovsky, Zhang. They fall into types by their intersection form, \$E_0, E_1 \ldots, E_6, E_7, E_8\$. Cherkis and Cross showed that the \$E_0, E_1, \ldots E_6\$ case arise from Doubly Periodic Monopoles. My work is in completing this to the \$E_7\$ and \$E_8\$ case.