The field of dynamical systems and machine learning is witnessing significant developments, with a focus on improving the interpretability and efficiency of models. Researchers are exploring new methods for analyzing and predicting complex systems, including the use of reproducing kernel Hilbert spaces, transformers, and Riemannian geometry. These approaches are enabling the development of more accurate and efficient models, with applications in areas such as system identification, forecasting, and control. Notable papers in this area include: Convergent Methods for Koopman Operators on Reproducing Kernel Hilbert Spaces, which introduces a general, provably convergent, data-driven algorithm for computing spectral properties of Koopman operators. T-SHRED: Symbolic Regression for Regularization and Model Discovery with Transformer Shallow Recurrent Decoders, which improves the performance of SHRED models by leveraging transformers and sparse identification of nonlinear dynamics. Riemannian generative decoder, which simplifies Riemannian representation learning by introducing a generative decoder that finds manifold-valued maximum likelihood latents with a Riemannian optimizer. Lipschitz Bounds for Persistent Laplacian Eigenvalues under One-Simplex Insertions, which establishes a uniform Lipschitz bound for the change in persistent Laplacian eigenvalues when one simplex is added, delivering the first eigenvalue-level robustness guarantee for spectral topological data analysis.