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The Hecke correspondence via Yang-Mills-Higgs flow lines

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Graeme Wilkin
Tue, 22/03/2022 - 13:45 - 15:30

The Hecke correspondence plays a central role in the Geometric Langlands program. In this talk I will show that the Hecke correspondence for Higgs bundles has a natural analytic interpretation in terms of spaces of flow lines for the Yang-Mills-Higgs functional. This requires first constructing ancient solutions to the Yang-Mills-Higgs flow, and then classifying the isomorphism classes that appear in this construction. Finally I will also describe a geometric criterion for distinguishing between broken and unbroken flow lines using secant varieties associated to the underlying Riemann surface.

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