Title: Quantizations and index theory
Speaker: Rudy Rodsphon
Speaker Info: Vanderbilt University
Brief Description: Pretalk at 1:00
Special Note:
Abstract:
Abstract: A way to describe succinctly (local) index theory on closed spin manifolds is the following slogan of Quillen : Dirac operators are a "quantization" of connections, and index theory is a "quantization" of the Chern character. For non necessarily spin manifolds, pseudodifferential operators and their symbolic calculus play a crucial role in the original proofs of the index theorem. However, symbols may also be viewed as a deformation quantization of functions on the cotangent bundle, which has led to other fruitful approaches to index theory through another "quantization" process. Even if both viewpoints originate from physics (more precisely from quantum mechanics), the methods used involve a priori rather different technologies. The upshot of the talk will be to see that these different theories might have more to tell to each other, and that far reaching index problems may be solved very directly from such an interaction.Date: Thursday, October 13, 2016