Qiu Shi Want (Oxford) will speak in the geometry seminar on 26th January, at 2pm on 26th January 2026. Qiu Shi’s title is “Computer-assisted construction of SU(2)-invariant cohomogeneity one Einstein metrics,” and his abstract is below.
In this talk, I will present a construction of a new family of SU(2)-invariant complete negative Einstein metrics on the complex line bundle O(-4) over CP^1. The metrics are conformally compact and generically neither Kähler nor self-dual. The proof involves using rigorous numerical techniques (Chebyshev polynomials and arbitrary-precision interval arithmetic) to produce an approximate Einstein metric to high precision in a bounded region near the singular orbit, then perturbing it to a genuine Einstein metric using fixed-point methods. At the boundary of this region, we show that the latter metric is sufficiently close to hyperbolic space so that it extends to a complete, asymptotically hyperbolic Einstein metric. Our construction is based on previous work of Buttsworth—Hodgkinson.