The current volume is a collection of contributions presented at the ICMAM Central America, the Caribbean 2025 conference and the AMATES–ICMAM Workshop 2025. The volume covers topics in applied analysis and mathematical physics. These topics include transportation models, Schrödinger–Poisson systems, and nonlinear PDEs with applications to semiconductor theory, quantum technologies, and optimization. The volume also features contributions in dynamical systems and network theory, essential for studying stability and long-term behavior in fields such as ecology, aerospace engineering, and neural networks. In addition, the volume features contributions in structural mathematics, with results in geometry (Kähler manifolds), algebra (representation theory), and combinatorics (graph theory), forming the foundation of much current progress in pure mathematics.

Duván Cardona Sanchez is a Colombian mathematician, a Professor of Mathematics at Pontificia Universidad Javeriana in Bogotá, Colombia, an FWO Research Fellow at Ghent University, Belgium, and an Oberwolfach Leibniz Fellow at the Oberwolfach Research Institute for Mathematics (MFO) in Germany. His research interests lie in harmonic analysis, partial differential equations, pseudodifferential operators, Fourier integral operators, and control theory..

Karina Navarro Gonzalez is a Mora Miriam Rozen Gerber research fellow at the Weizmann Institute of Science, Israel. Her research interests include functional analysis, function spaces, and general problems in analysis and partial differential equations.

Brian Grajales is a Colombian mathematician and Professor at the Universidade Estadual de Maringá, Brazil. His research spans differential geometry and Lie theory, with emphasis on Riemannian geometry on homogeneous spaces. 

Santiago Correa is a postdoctoral researcher at the University of Augsburg, Germany. His research focuses on mathematical analysis, PDEs, and their applications.

Dimas Tejada is a Salvadoran mathematician and director of the School of Mathematics at the University of El Salvador. His research interests include Dynamical Systems and Differential Geometry, with emphasis on the behavior of principal lines on smooth manifolds immersed in three-dimensional Minkowski space. 

Yoceman Sifontes is a Salvadoran mathematician and lecturer at the mathematics department of the American School of El Salvador. His research focuses on the dynamics of Kleinian groups and their extensions to the ideal boundary.