Deadline for manuscript submissions: 30 June 2026

 

Special Issue Editors

Dr. Álvaro Antón-Sancho  Website  E-Mail: alvaro.anton@frayluis.com
Guest Editor
Catholic University of Ávila, Spain                
Interests: principal bundles; vector bundles; algebraic curves; riemann surfaces; higgs bundles; automorphisms; fixed points; stratifications

      

Special Issue Information

Dear colleagues,

 

The geometry of fiber, vector, and principal bundles over manifolds has become a pivotal framework at the intersection of differential geometry, analysis, and mathematical physics. This approach offers powerful tools for studying differential equations and control processes, which are relevant to understanding complex dynamical systems. The interplay between bundle structures and differential systems has yielded significant theoretical developments and practical applications in fields such as geometric mechanics, quantum control, and gauge field theories. 

This special issue aims to showcase recent progress and stimulate innovative research at the crossroads of geometry and control. By gathering diverse perspectives and methodologies, it seeks to foster interdisciplinary dialogue and collaboration, enriching both the theoretical foundations and applied aspects of the field. The contributions will serve as a valuable reference for researchers and practitioners interested in the geometric formulation of differential systems and control problems.

Submissions of original research articles and comprehensive reviews are encouraged, particularly those addressing novel applications or theoretical advances in the geometry of bundles and their role in differential equations and control. The goal is to highlight emerging directions, bridge conceptual gaps across disciplines, and inspire future developments in mathematics, engineering, and physics.

Potential topics include, but are not limited to:

-Connections and curvature in vector bundles
-Jet bundles and differential operators in PDEs
-Principal bundles and gauge-theoretic methods
-Lie groupoids and Lie algebroids in control theory
-Symplectic and Poisson geometry in bundle contexts
-Variational problems on fibered manifolds
-Differential invariants and conservation laws
-Geometric integration techniques for systems on bundles
-Singular perturbation methods in bundle frameworks
-Asymptotic analysis of bundle-based differential systems
-Geometric control theory for principal and associated bundles
-Optimal control formulated via bundle geometry
-Hamiltonian and Lagrangian systems with control aspects
-Sub-Riemannian geometry and nonholonomic constraints
-Quantum control through bundle-theoretic approaches
-Applications in mathematical physics, including gauge fields and gravitation
-Bundle-based methods in biological and complex systems
-Mechanical systems with symmetries and reduction techniques
-Numerical algorithms inspired by bundle geometry
-Machine learning techniques in geometric control

Keywords: fiber bundles, vector bundles, principal bundles, differential equations, geometric control theory, jet bundles, Lie groupoids, gauge theory, variational calculus, Poisson geometry, quantum control, differential invariants

 

Guest Editor

Dr. Álvaro Antón-Sancho

 

 

 Published Papers