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Some Remarks on Yang–Mills Type Equations in Higher Dimensions

[HYBRID WORKSHOP] New Four-Dimensional Gauge Theories October 24, 2022 - October 28, 2022

October 28, 2022 (02:00 PM PDT - 03:00 PM PDT)
Speaker(s): Richard Wentworth (University of Maryland)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Tags/Keywords
  • Hermitian-Yang-Mills connections

  • Bogomolov inequality

  • Higgs bundle

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Some Remarks On Yang–Mills Type Equations In Higher Dimensions

Abstract

The talk consists of two parts. First, I will discuss a variant of anti-self-dual connections in higher dimensions that is motivated by calibrated geometry and multipolarizations in Kaehler geometry. Such connections are shown to satisfy a version of Uhlenbeck weak compactness. In the case of Hermitian manifolds, we prove analogs of the Donaldson–Uhlenbeck–Yau and nonabelian Hodge theorems. Second, I describe an extension of the Donaldson–Uhlenbeck–Yau theorem to normal projective varieties. Taken together, the two parts give an analytic proof of Miyaoka’s version of the Bogomolov–Gieseker inequality, with a sharp result in the case of equality. This is joint work with Xuemiao Chen.

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Some Remarks On Yang–Mills Type Equations In Higher Dimensions

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