Caltech Home > PMA Home > Master Calendar > Math Graduate Student Seminar
Search
Friday, May 17, 2019
12:00 PM - 1:00 PM
Linde Hall 255

Math Graduate Student Seminar

A twisted local index formula for curved noncommutative two tori
Jim Tao, Department of Mathematics, Caltech,

We consider the Dirac operator of a general metric in the canonical conformal class on the noncommutative two torus, twisted by an idempotent (representing the K-theory class of a general noncommutative vector bundle), and derive a local formula for the Fredholm index of the twisted Dirac operator. Our approach is based on the McKean-Singer index formula, and explicit heat expansion calculations by making use of Connes' pseudodifferential calculus. As a technical tool, a new rearrangement lemma is proved to handle challenges posed by the noncommutativity of the algebra and the presence of an idempotent in the calculations in addition to a conformal factor.

For more information, please contact Math Department by phone at 626-395-4335 or by email at mathinfo@caltech.edu.