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Explore the deep connections between four-manifold invariants and supersymmetric field theory in this advanced differential geometry and physics seminar. Begin with a comprehensive review of topological twisting as a choice of background fields, then examine the standard paradigm for formulating Donaldson invariants as correlation functions in twisted supersymmetric N=2 d=4 quantum field theory. Learn about the quantum field theory derivation of the relationship between Donaldson invariants and Seiberg-Witten invariants, and discover what insights can be gained from other twisted quantum field theories. Investigate new results on four-manifold invariants derived from N=2 supersymmetric quantum chromodynamics (QCD), and advance to 5-dimensional theories and their associated "K-theoretic Donaldson invariants." Examine 6-dimensional theories and "elliptic Donaldson invariants," and explore the extension to families of four-manifolds where coupling to suitably twisted and truncated superconformal gravity produces invariants valued in the cohomology of the classifying space of the diffeomorphism group of the four-manifold.
