Priority Programme “Combinatorial Synergies” (SPP 2458)
Deadline: 25. September 2023
In March 2023, the Senate of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) established the Priority Programme “Combinatorial Synergies” (SPP 2458). The programme is designed to run for six years. The present call invites proposals for the first three-year funding period.
Combinatorics is the study of finite and discrete structures. Starting from fundamental questions of ordering, decomposing and structuring finitely many objects or states, combinatorics has evolved into a nanotechnology of mathematics and its applications. Due to its interdisciplinarity, it is a highly interactive core mathematical area. Research questions are unified, and structurally related approaches are developed into unifying theories with intrinsic questions and methods.
The present availability of complex mathematical observations induces a fundamental transformation of mathematical research in the interplay of data and structure. This Priority Programme will form a combinatorics network in Germany that guides this transformation. The programme will enable breakthrough advances within and across the thematic areas described below. The accessibility and usability of research data will enable the creation of a globally visible combinatorics network.
The individual projects in this Priority Programme must concern combinatorial synergies in themes ranging from fundamental mathematics research to applications. The programme evolves around the following themes: enumeration, Dynkin classification, commutative algebra, matroids, convexity, lattice points, statistics, non-linear optimisation and mathematical physics. Important impulses are expected to evolve from innovative developments within the main themes and their interconnections. Possible synergies include: Weyl groups, face vectors, Kähler packages, combinatorial polytopes, amplituhedra, combinatorial commutative algebra, Ehrhart theory, Lorentzian polynomials, Coxeter-Catalan structures, hyperplane arrangements, the E8-lattice, positroids and many more.
Extremal combinatorics, additive combinatorics and related themes are not in the focus of this Priority Programme.