Advances in Combinatorics, Tropical Geometry and Geometry of Matroids
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "B: Geometry and Topology".
Deadline for manuscript submissions: 22 July 2026 | Viewed by 8
Special Issue Editors
Interests: tropical geometry; real algebraic geometry; geometry of matroids; algebraic combinatorics
Special Issue Information
Dear Colleagues,
Combinatorics, tropical geometry, and the geometry of matroids are vibrant and rapidly developing areas of mathematics that play a central role in both theoretical advances and applications. These fields are deeply interconnected, offering powerful tools for understanding algebraic, geometric, and topological structures, while also providing new perspectives on problems arising in optimization, representation theory, and beyond.
This Special Issue aims to bring together a diverse set of contributions that demonstrate the depth and breadth of these interconnected fields, while celebrating 25 years of tropical geometry. Both theoretical and applied perspectives are encouraged. Topics include, but are not limited to, the following:
- Matroid theory, geometry of matroids, and connections to topology and polyhedral geometry;
- Tropical geometry: intersection theory, moduli, invariants (e.g., CSM classes), and applications in algebraic geometry, number theory, and optimization;
- Computational and algorithmic algebraic geometry; symbolic and numeric methods supporting experimentation;
- Chern–Schwartz–MacPherson classes, characteristic cycles, and related invariants;
- Toric and Schubert geometry and interactions with representation theory;
- Combinatorics of polytopes, fans, and Coxeter/cluster structures;
- Enumerative problems in tropical and matroidal settings;
- Algebra and geometry over the “field with one element”;
- Applications to singularity theory, moduli problems, and related areas;
- Connections between tropical geometry, representation theory, and mathematical physics.
Dr. Lucía López de Medrano
Dr. Manchun Leung
Guest Editors
Manuscript Submission Information
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Keywords
- combinatorics
- tropical geometry
- geometry of matroids
- polyhedral geometry
- computational geometry
- algorithmic algebraic geometry
- Chern–Schwartz–MacPherson classes
- toric geometry
- Schubert geometry
- representation theory
- combinatorics of polytopes and fans
- coxeter/cluster structures
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