| A | Mathematical challenges requiring software support | |
| A1 | Character sheaves and generic character tables | Group representation theory | Meinolf Geck, Frank Lübeck |
| A2 | Generalised Gelfand-Graev representations, unipotent classes and nilpotent orbits | Group representation theory | Meinolf Geck, Gunter Malle |
| A5 | Decomposition matrices | Group representation theory | Gunter Malle |
| A10 | Algorithmic approaches to Teichmüller curves | Algebraic geometry | Gabriela Weitze-Schmithüsen |
| A11 | Tropical linear degenerate flag varieties and applications | Tropical geometry, representation theory | Ghislain Fourier, Hannah Markwig, Gabriele Nebe |
| A13 | Generating series for curve counting | Tropical geometry | Janko Böhm, Hannah Markwig |
| A14 | Topological recursion and free probability theory | Free probability, random matrices | Roland Speicher |
| A17 | Clifford orders | Number theory | Gabriele Nebe |
| A19 | Practical and theoretical aspects of the group isomorphism problem | Algorithmic group theory, finite group theory, computational complexity | Pascal Schweitzer |
| A20 | Towards unipotent character sheaves associated to Coxeter groups | Representation theory, category theory | Ulrich Thiel |
| A21 | Arithmetic and convexity in buildings | Tropical geometry, arithmetic geometry, number theory | Gabriele Nebe, Bernd Sturmfels |
| A22 | Automorphisms of irreducible holomorphic symplectic manifolds via hermitian forms | Algebraic geometry, number theory | Simon Brandhorst |
| A23 | Conjectures and new examples in birational geometry | Algebraic geometry, representation theory | Vladimir Lazic, Frank-Olaf Schreyer, Ulrich Thiel |
| A24 | Lattice polytopes, partially ordered sets, spherical varieties | Polyhedral and algebraic geometry, representation theory | Michael Joswig, Ghislain Fourier |
| A25 | Quantum Symmetries and Quantum Isomorphisms of Graphs | Compact Quantum Groups | Moritz Weber |
| A26 | Algorithms and Logic for Automata Groups | Geometric group theory, decision problems, finite state automata | Laurent Bartholdi |
| B | Computational challenges posed by research in mathematics | |
| B1 | Central software project: Interaction, high-performance and support (OSCAR) | Algorithmic number theory, group representation theory, polyhedral geometry, algebraic geometry, computer algebra | Wolfram Decker, Claus Fieker, Max Horn, Michael Joswig |
| B2 | Galois cohomology for non-normal fields | Algorithmic number theory | Claus Fieker |
| B4 | Enumerating tropical curves and hypersurfaces | Tropical geometry | Michael Joswig, Hannah Markwig |
| B5 | Singular: Massively parallel structures in algebraic geometry | Algebraic geometry, computer algebra | Janko Böhm, Simon Brandhorst, Wolfram Decker |
| B6 | Gröbner techniques for PBW deformations: parametrization, representations, applications | Computer algebra, representation theory, constructive homological algebra | Ghislain Fourier, Ulrich Thiel, Eva Zerz |
| B7 | Computations with matrix groups | Group theory | Max Horn, Alice Niemeyer |
| C | Central projects | |
| IRTG | Integrated Research Training Group | | Gabriele Nebe, Roland Speicher |
| Z | Central tasks of the Collaborative Research Centre | | Gunter Malle |
