Equivariant Local Index Theory for Lie Groupoids

Explore equivariant local index theory for Lie groupoids in this 56-minute seminar talk from the Global Noncommutative Geometry Seminar. Delve into topics such as motivation, local index theory, equivariant index theory, Euler Duram operator, complexified Clifford bundle, Dirac operators, and Gamma operators. Examine heat flow, Clifford algebra, and the process of computing traces. Investigate symbol calculus, simple calculus, and the algebraic approach, including Guesser calculus. Learn about the heat kernel, super trace, and the main theorem. Discuss analogs, rescaled modules, and code dimension formula. Engage with questions and gain insights into this advanced mathematical topic.

Introduction
Motivation
Local Index Theory
Equivariant Index Theory
Euler Duram Operator
Complexified Clifford Bundle
Dirac Operators
Gamma Operators
Heat Flow
Clifford Algebra
Computing Traces
Symbol Calculus
Simple Calculus
Algebraic Approach
Guesser Calculus
The Symbol Calculus
The Heat Kernel
The Super Trace
The Theorem
Analogs
Rescaled Modules
Questions
Code Dimension
Formula