Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
New minimal surfaces in hyperkähler 4-manifolds
I will describe the construction of new minimal surfaces in hyperkähler 4-manifolds arising from the Gibbons–Hawking Ansatz, i.e. hyperkähler 4-manifolds that admit a triholomorphic circle action, and on certain K3 surfaces. The minimal surfaces we produce are obtained via a gluing construction using well-known surfaces, the Scherk surface in flat space and the holomorphic cigar in the Taub-NUT space, as building blocks. The minimal surfaces obtained via this construction are not holomorphic with respect to any complex structure compatible with the metric, are not circle invariant, they can be parameterized by a harmonic map that satisfies a first-order
Fueter-type PDE, and yet are unstable. This is joint work with Federico Trinca.