| A | Mathematical challenges requiring software support | |
| A1 | Character sheaves and generic character tables | Group representation theory | Meinolf Geck, Frank Lübeck, Gunter Malle |
| A5 | Decomposition matrices | Group representation theory | Gunter Malle |
| A10 | Algorithmic approaches to Teichmüller curves | Algebraic geometry | Laurent Bartholdi, Gabriela Weitze-Schmithüsen |
| A11 | Linear degenerate flag varieties and their tropical counterparts | Tropical geometry, representation theory | Xin Fang, Ghislain Fourier, Hannah Markwig |
| A13 | Plane Hurwitz numbers | Algebraic geometry, tropical geometry | Daniele Agostini, Janko Böhm, Hannah Markwig |
| A17 | Generic orthogonal character tables | Group representation theory, number theory | Meinolf Geck, Gabriele Nebe |
| A20 | Categorical representation theory | Representation theory, category theory | Ulrich Thiel, Moritz Weber |
| A22 | Effective Torelli Theorems | Algebraic geometry | Daniele Agostini, Simon Brandhorst |
| A23 | Algorithmic Minimal Model Program | Algebraic geometry | Janko Böhm, Vladimir Lazić |
| A24 | Lattice polytopes and representation theory | Polyhedral and algebraic geometry, representation theory | Michael Joswig, Xin Fang, Ghislain Fourier |
| A25 | Homomorphism counts for graphs and groups, classical and quantum | Compact quantum groups, algebraic combinatorics, computational quantum information theory | Pascal Schweitzer, Moritz Weber |
| A26 | Algorithms and logic for groups and dynamical systems | Geometric group theory | Laurent Bartholdi |
| B | Computational challenges posed by research in mathematics | |
| B1 | Central software project: OSCAR | Algorithmic number theory, group representation theory, polyhedral geometry, algebraic geometry, computer algebra | Simon Brandhorst, Claus Fieker, Tommy Hofmann, Max Horn, Michael Joswig |
| B2 | Explicit class field theory in local fields | Algorithmic number theory | Claus Fieker |
| B4 | Computations in tropical combinatorics | Polyhedral and
tropical geometry | Michael Joswig, Gabriele Nebe |
| B5 | Singular: Local-to-global Stuctures in Algebraic Geometry and Applications | Algebraic geometry, computer algebra | Janko Böhm, Simon Brandhorst |
| B7 | Computations with matrix groups | Group theory | Max Horn, Alice Niemeyer |
| B8 | Effective difference algebra and difference algebraic groups | Computer algebra,Computer algebra,
ring theory,
representation theory | Annette Bachmayr, Daniel Robertz |
| C | Central projects | | |
| IRTG | Integrated Research Training Group | | Gabriele Nebe, Moritz Weber |
| Z | Central tasks of the Collaborative Research Centre | | Gunter Malle |
