This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas’ students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.

Following in the Footsteps of Ronald G. Douglas.- Functional Models for Commuting Hilbert space Contractions.- The Extended Aluthge Transform.- Open Problems in Wavelet Theory.- When is Every Quasi-multiplier a Multiplier?.- Isomorphism in Wavelets II.- Nevanlinna-Pick Families and Singular Rational Varieties.- On Certain Commuting Isometries, Joint Invariant Subspaces and C*-algebras.- Spectral Analysis, Model Theory and Applications of Finite-Rank Perturbations.- Invariance of the Essential Spectra of Operator Pencils.- Decomposition of the Tensor Product of two Hilbert Modules.- A Survey on Classification of C*-Algebras with the Ideal Property.- A Survey on the Arveson-Douglas Conjecture.- Cauchy-Riemann Equation for Free Noncommutative Functions.- Uniform Roe Algebras and Geometric RD Property.- Integral Curvature and Similarity of Cowen-Douglas Operators.- Singular Subgroups in widetilde{A}_2-groups and Their von Neumann Algebras.- A K-theoretic Selberg Trace Formula.- Singular Hilbert Modules on Jordan-Kepler Varieties.- A Survey of Ron Douglas’s Contributions to the Index Theory of Toeplitz Operators.- Differential Subalgebras and Norm-controlled Inversion.- Hermitian Metrics on the Resolvent Set and Extremal Arc Length.- Hybrid Normed Ideal Perturbations of n-tuples of Operators II: Weak Wave Operators.- An Introduce to Curvature Inequalities for Operators in the Cowen-Douglas Class.- Reproducing Kernel of the Space R^t(K,mu).