Real Algebraic Geometry and Its Applications

Dear Colleagues,

This Special Issue explores the theoretical field of real algebraic geometry and its interactions with other fields. Real algebraic geometry provides theoretical frameworks and computational tools that transform applied fields through its fundamental structures—such as semi-algebraic sets, real varieties, toric geometry, and related algorithms. These mathematical approaches have applications in several fields of science and engineering, offering elegant solutions to complex problems. Thus, recent advances have enabled the achievement of breakthroughs in motion planning, geometric vision problems, robotic manipulation, machine learning, topological data analysis, and verification methods, among others, creating new research opportunities at this interdisciplinary frontier.

This Special Issue welcomes original research contributions that showcase real algebraic geometry developments and innovative applications in any field of science or engineering, as well as theoretical developments inspired by challenges in these domains. We particularly encourage the submission of works that bridge the gap between mathematical theory and practical implementation, demonstrating how algebraic methods can enhance robustness, efficiency, and capabilities in real-world systems.

Contributions on the following topics are particularly welcome, though the list is not exhaustive.

Theoretical Foundations:

• Semi-algebraic geometry for configuration spaces;
• Real algebraic varieties and stratifications;
• Computational aspects of real algebraic geometry;
• Toric varieties and their applications;
• Effective algorithms for polynomial systems over the reals;
• Automorphisms of algebraic varieties and fixed points;
• Group actions on real algebraic varieties.

Applications:

• Kinematic and dynamic modeling using algebraic methods;
• Robot motion planning with algebraic guarantees;
• Singularity analysis of mechanisms;
• Multi-view geometry and camera models;
• Structure from motion and SLAM using algebraic methods;
• Three-dimensional reconstruction algorithms with optimality guarantees;
• Integration of algebraic methods with deep learning;
• Topological data analysis for robotics and vision;
• Verification and certification using real algebraic geometry;
• Privacy-preserving vision algorithms with algebraic foundations;
• Algebraic techniques for sensor fusion;
• Computational complexity and approximation algorithms.

Dr. Alvaro Anton-Sancho
Guest Editor

Manuscript Submission Information

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