**Date/Time**

Date(s) - 14/09/2023*4:30 pm - 5:30 pm*

**Speaker**: Hari Kunduri ( McMaster)

**Title: **Existence and uniqueness of toric gravitational instantons

**Abstract: **A gravitational instanton is a four-dimensional complete, non compact Ricci flat manifold (M,g). Typically one is interested in solutions that decay to a flat metric near infinity. Two notable classes are the so-called asymptotically locally Euclidean (ALE) families, which approach R^4/K where K is a finite subgroup of SU(2), or asymptotically flat (AF) spaces which approach S^1 X R^3 (one may also consider non trivial circle bundles). I will discuss uniqueness and existence theorems for instantons of these types with a torus symmetry. Solutions are characterised by data that encodes the fixed point sets of the torus action. Furthermore, we establish that for every admissible rod structure there exists an instanton that is smooth up to possible conical singularities at the axes of symmetry. This is in sharp contrast to the analogous problem in the Lorentzian setting (stationary and axisymmetric black hole solutions).

**Location** : HH 312