SPP 2458:  Combinatorial Synergies

• Subject Area: Mathematics ; Biology ; Computer Science, Systems and Electrical Engineering
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 521249412

Combinatorics is the study of finite and discrete structures. Starting from fundamental questions about orderings, decompositions and structures of finitely many objects or states, combinatorics represents the nanotechnology of mathematics and its applications. Due to its interdisciplinarity, it is a central mathematical research area with influence across disciplinary boundaries. Questions are unified and sound theories with intrinsic questions and methods are developed from structurally related approaches. Discrete data has always been a source for the development of mathematical theories. Their analysis is comparable to the derivation of physical laws from observations of phenomena in nature. Due to the complexity of mathematical observations we are at the beginning of a revolution for the development cycles in the interplay between data and structure. This priority program identifies the following nine thematic directions guiding and organizing the research efforts. These are Enumeration, Dynkin Classification, Commutative Algebra, Matroids, Convexity, Lattice Points, Statistics, Non-linear Optimization, and Mathematical Physics. This program links the huge potential of excellent and dynamic combinatorics groups. It will enable breakthrough advances within and across the thematic areas. In the process, the accessibility and usability of discrete data will act as a multiplier. A globally visible combinatorics network in modern basic mathematical research will be created.

• DFG Programme: Priority Programmes
• International Connection: Israel, Italy, Japan, Norway, Switzerland

Projects

• Combinatorial and probabilistic aspects of symmetric edge and cosmological polytopes (Applicants Juhnke-Kubitzke, Martina ;  Thäle, Christoph )
• Combinatorial Hodge theory in singularity theory and toric geometry (Applicant Sevenheck, Christian )
• Combinatorial Methods for Learning Max-Linear Bayesian Networks (Applicants Améndola Cerón, Carlos ;  Hollering, Ph.D., Benjamin )
• Compartmentalized structures (Applicant Sanyal, Raman )
• Compute the equivariant Orlik-Solomon algebra of a matroid (Applicant Barakat, Mohamed )
• Convexity and Grassmannians in Statistical Inference (Applicant Wahl, Martin )
• Coordination Funds (Applicant Stump, Christian )
• Counting permutation and chirotope patterns: algorithms, algebra, and applications (Applicant Diehl, Joscha )
• Extremal bodies with respect to lattice functionals (Applicants Averkov, Gennadiy ;  Codenotti, Giulia ;  Freyer, Ansgar )
• Finding short polynomials (Applicant Kahle, Thomas )
• Invariant chains in algebra and discrete geometry (Applicant Römer, Tim )
• K-Theory and Normal Complexes (Applicant Haase, Christian )
• Kähler Package for the Grassmann Zonoid Algebra (Applicants Breiding, Paul ;  Bürgisser, Peter )
• Local Ehrhart Theory and its Synergies (Applicant Nill, Benjamin )
• Lorentzian polynomials and equality in log-concave inequalities (Applicants Süß, Hendrik ;  Wannerer, Thomas )
• Machine learning combinatorial statistics and maps (Applicant Stump, Christian )
• New tools from combinatorial topology, sheaf theory and homological algebra for the study of hyperplane arrangements and oriented matroids (Applicant Mücksch, Paul )
• On connected subgraph arrangements (Applicant Röhrle, Gerhard )
• On the combinatorics and geometry of (sub-) groups generated by reflections (Applicant Baumeister, Barbara )
• On Ziegler Extensions of Multiarrangements (Applicant Röhrle, Gerhard )
• Positive Geometry (Applicant Sinn, Rainer )
• Random Lattice Polytopes (Applicant Reitzner, Matthias )
• Rethinking Tropical Linear Algebra: Buildings, Bimatroids, and Applications (Applicant Ulirsch, Ph.D., Martin )
• Simpliciality in Arrangements and Matroids (Applicants Cuntz, Michael ;  Kühne, Lukas ;  Sanyal, Raman )
• Sums of Nonnegative Circuit Polynomials and Combinatorics in Polynomial Optimization (Applicants Theobald, Thorsten ;  de Wolff, Timo )
• Tropical Data in Combinatorial Algebraic Geometry (Applicant Geiger, Alheydis )
• Wachspress Coordinates: a bridge between Algebra, Geometry and Combinatorics (Applicant Winter, Martin )

• Spokesperson: Professor Dr. Christian Stump