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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.