Title: Widom's pseudo differential calculus and its applications
Speaker: Yang Liu (OSU)
Abstract: As a part of the program of exploring intrinsic curvatures for noncommutative manifolds, the author constructed a pseudo differential calculus which is suitable for spectral geometry on toric noncommutative manifolds. Such symbol calculus for pseudo differential operators is obtained by deforming an intrinsic (coordinate-free) symbol calculus developed by H. Widom in 1978. In this talk, we will outline Widom's construction of such symbol calculus and then apply the calculus to compute first few heat expansion coefficients of the squared Dirac operator acting on a spinor bundle. The ultimate goal is to upgrade such calculation to four dimensional toric noncommutative manifolds to achieve a closed formula for the log-determinant functional associated to a Laplacian type operator with a noncommutative conformal perturbation. The question is open even for the case of noncommutative four tori.
