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Consortium Distinguished Lecture Series
Nigel Hitchin

Spinor-valued Higgs Bundles

Nigel Hitchin, University of Oxford

Friday, December 8, 2023, 5:00pm

Ungar Building, Room 528B

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Abstract: The theory of Higgs bundles has over the last 35 years shed light on many aspects of the geometry of vector bundles on Riemann surfaces. This involved the study of endomorphisms twisted by the canonical bundle. The talk will consider what happens when we twist with a square root of the canonical bundle - this can be considered as solutions of a Dirac equation on the Riemann surface. Some aspects of the standard theory apply directl but others are very different.

ALE metrics and nodal curves

Monday, December 11, 2023, 5:00pm

Lakeside Village Auditorium, University of Miami

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Abstract: Kronheimer constructed asymptotically locally Euclidean metrics on the resolution of a Kleinian singularity by a hyperk\”ahler quotient construction. This talk involves an alternative approach using the algebraic geometry of the twistor space and the circle action on the resolution. It leads to the consideration of nodal curves in a linear system on a rational surface, and from that to the differential geometry of the three-dimensional quotient of the ALE space.