The field of membrane wrinkling and algorithmic analysis is experiencing significant developments, with a focus on improving the accuracy and efficiency of models and algorithms. Researchers are exploring new approaches to membrane wrinkling, such as variationally consistent models based on spectral decomposition of the stress tensor, which offer enhanced generality and improved performance under various loading conditions. In the realm of algorithmic analysis, smoothed analysis is being applied to various algorithms, including the simplex method, to better understand their performance in practice. This has led to the development of new algorithms with improved noise dependence and optimal running times. Furthermore, advances in radial isotropic positioning and domain decomposition methods are enabling faster and more accurate computations, with applications in functional analysis, communication complexity, and learning algorithms. Notable papers include:

• A variationally consistent membrane wrinkling model that improves accuracy and offers enhanced generality.
• An optimal smoothed analysis of the simplex method, which achieves a better noise dependence and running time.
• A faster algorithm for computing approximate Forster transforms, with applications in radial isotropic positioning.