The field of numerical methods for partial differential equations (PDEs) and geometric modeling is experiencing significant advancements. Recent research has focused on developing fast and efficient solvers for boundary integral equations, preconditioning techniques for high-frequency Maxwell equations, and innovative approaches to shape modeling and curve length minimization. Notable innovations include the use of hierarchical direct solvers, proxy-based approximations, and differentiable function representations. These advancements have the potential to improve the accuracy and efficiency of numerical simulations in various fields, including physics, engineering, and computer science. Noteworthy papers include: A Fast Direct Solver for Boundary Integral Equations Using Quadrature By Expansion, which introduces a hierarchical direct solver for linear systems arising from boundary integral equations. PyFRep: Shape Modeling with Differentiable Function Representation, which proposes a framework for performing differentiable geometric modeling based on the Function Representation (FRep).