主题词：Geometric and Algebraic Topology; Homotopy and Cohomology in Algebraic Topology; Algebraic structures and combinatorial models; Algebraic Geometry and Number Theory; Mathematical Dynamics and Fractals; Advanced Operator Algebra Research; Advanced Combinatorial Mathematics; Geometry and complex manifolds; Geometric Analysis and Curvature Flows; Advanced Topics in Algebra; Advanced Algebra and Geometry; Topological and Geometric Data Analysis; Polydiacetylene-based materials and applications; Diverse Scientific and Economic Studies; Human auditory perception and evaluation; Finite Group Theory Research; Educational Robotics and Engineering; semigroups and automata theory; Analytic and geometric function theory; Computational Geometry and Mesh Generation; Advanced Topology and Set Theory; Photonic Crystals and Applications; Botulinum Toxin and Related Neurological Disorders; Black Holes and Theoretical Physics; Polynomial and algebraic computation