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Abstract

This thesis consists of four research papers stapled together. 1. Annular Homology of Artin Braids I. 2. Annular Homology of Artin Braids II: Springer Fibers. 3. Annular Homology of Artin Braids III: Rational Cherednik Algebras. 4. Algebraic Braids and the Springer Theory of Hitchin Systems.

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