Pseudodifferential operators and complex powers of elliptic operators on noncommutative tori
May 16, 2019
W303 School of Mathematics, Sichuan University
Gihyun Lee (Seoul National Univesity)
In the early 1980s A. Connes introduced a pseudodifferential calculus on noncommutative tori. The first goal of this mini-course is to give a detailed account on this calculus. I will also explain generalizations of Connes' pseudodifferential calculus, namely, pseudodifferential operators with parameter and holomorphic families of pseudodifferential operators. The last part of this mini-course will be devoted to the construction of complex powers of elliptic pseudodifferential operators on noncommutative tori.
All notions listed above are essential tools in the differential geometry study of noncommutaitve tori initiated by A. Connes and P. Tretkoff. So this mini-course will provide us with a solid analytic background on this research field. Based on a joint work with H. Ha and R. Ponge.