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Marc Levine: Bott residue theorems in quadratic intersection theory,applications
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https://youtu.be/TBI6ApRckdU?si=4bT7GuO5WZgjS88u This talk was part of the workshop "Motivic and non-commutative aspects of enumerative geometry" and the conference "Homotopy theory, K-theory, and trace methods" held in July 2023 at Radboud University, Nijmegen, The Netherlands. The latter conference was held in honor of Bjørn Ian Dundas' 60th birthday. Abstract: Torus localization has been a useful tool for computing characteristic classes in many settings. We will describe some background for “quadratic intersection theory”, which is an intersection theory that replaces the role of the integers, as coefficients, intersection multiplicities or degrees, with quadratic forms. In this context, we have developed quadratic versions of the Atiyah-Bott localization theorem, the Bott residue formula and Graber-Pandharipande localization of virtual fundamental classes; these have been extended in scope by Alessandro D’Angelo. We describe these results and applications to some counting problems, such as twisted cubics on hypersurfaces, and computations of some quadratic Donaldson-Thomas invariants. The work on twisted cubics is joint with Sabrina Pauli and computations of quadratic DT invariants are due to Anneloes Viergever.
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