The field of geometric computing and nonlinear analysis is witnessing significant advancements, driven by the development of innovative numerical methods and deep learning frameworks. Researchers are exploring new approaches to analyze and process complex geometric data, including surfaces with non-trivial topology and high-genus surfaces. The use of harmonic maps, Morse sequences, and convolutional neural networks is becoming increasingly prominent in this field. These techniques enable the efficient computation of optimal homeomorphisms, the analysis of topological features, and the solution of nonlinear problems with high accuracy. Noteworthy papers in this area include: A Structure-Preserving Numerical Method for Harmonic Maps Between High-genus Surfaces, which develops a novel algorithm for computing harmonic maps between closed surfaces. A Convolutional Hierarchical Deep-learning Neural Network (C-HiDeNN) Framework for Non-linear Finite Element/Meshfree Analysis, which introduces a convolution operator to enhance the approximation of nonlinear finite element and meshfree analysis.