On automorphisms of complex $b^k$-manifolds
Foundations of symplectic $b^k$-geometry were laid by Guillemin et al and has its roots in the $b$-calculus of Melrose. In a similar spirit, complex $b$-calculus was worked out by Mendoza. In this talk, we discuss the local and global automorphisms of complex $b^k$ upper half planes. We consider analogues of weighted Bergman spaces and associated Toeplitz operators as well as coherent states. This is joint work with Tatyana Barron.