1. The Local Index Theorem and the Tangent Groupoid Open Access Author: Haj Saeedi Sadegh, Ahmad Reza Title: The Local Index Theorem and the Tangent Groupoid Graduate Program: Mathematics Keywords: Index TheoremGroupoidSpinorsDirac OperatorCyclic CohomologyRescaled BundleRescalingHarmonic OscillatorHeat Equation File: Download My_Dissertation.pdf Committee Members: Murat Gunaydin, Outside Unit & Field MemberPing Xu, Major Field MemberNigel Higson, Chair & Dissertation AdvisorNathanial Brown, Major Field MemberAlexei Novikov, Professor in Charge/Director of Graduate Studies