No. Project title Research area
IMathematical challenges requiring software support
I.1 Fourier matrices and character sheavesGroup representation theory
I.2Generalised Gelfand-Graev representations in bad characteristicGroup representation theory
I.3Imprimitive representations of quasisimple finite reductive groupsRepresentation theory, group theory
I.4 Decomposition matrices for exceptional groups of Lie typeGroup representation theory
I.5 Derived categories of equivariant coherent sheavesAlgebraic geometry, constructive homological algebra, computer algebra
I.6Syzygies and cohomologyAlgebraic geometry, computer algebra
I.7Construction of random points in moduli spaces and their geometryAlgebraic geometry, computer algebra
I.8Algorithmic approaches to Teichmüller curvesAlgebraic geometry
I.9Moduli spaces of tropical varieties, modifications and compactificationsTropical geometry
I.10Tropical mirror symmetry of elliptic curvesTropical geometry
I.11Random matrices and Hurwitz numbersFree probability, random matrices, tropical geometry
I.12Non-commutative rational functionsFree probability, random matrices
I.13Computational classification of orthogonal quantum groupsOperator algebras, compact quantum groups
I.14Unit groups of ordersAlgebraic number theory, arithmetic groups
IIComputational challenges posed by research in mathematics
II.1Central software project: Interaction, high-performance and supportAlgorithmic number theory, group representation theory, polyhedral geometry, algebraic geometry, computer algebra
II.2ANTIC: Explicit field constructionAlgorithmic number theory
II.3GAP: Generic character table of Spin+8(q)Group representation theory
II.4polymake: polyhedral data, quotients and stacksPolyhedral geometry
II.5Singular: A new level of abstraction and performanceAlgebraic geometry, computer algebra
II.6Gröbner bases and their applications over non-commutative ringsNon-commutative associative rings and algebras
IIICentral projects
MGKIntegrated research training group
ZCentral tasks of the Collaborative Research Centre