Representation theory is a cross-disciplinary branch of mathematics with a wide range of applications in mathematics and in the sciences. Chemistry uses representation theory for instance to investigate symmetries of molecules, while quantum mechanics is a classical area of applications in physics. Further applications in physics and related areas include integrable lattice models, the theory of elementary particles, random matrix theory, string theory and quantum computing. Among the many branches of mathematics heavily using representation theory are algebraic geometry, topology, number theory and differential geometry. Frobenius founded representation theory at the end of the 19th century when studying finite groups. At the beginning of the 20th century pioneers like Schur, Burnside, Cartan, Killing, Weyl, Noether and Brauer established fundamental concepts, objects and definitions. Today, representation theory is universally applicable and enjoys a variety of implementations; this makes representation theory truly interdisciplinary and turns it into a principle of order in mathematics and science. Since the beginnings of representation theory, it has seen several crucial changes in points of view, in concepts and in approaches. This has led to new branches forming and to areas changing their directions. In recent years, the various branches of representation theory have started to move towards each other, and this process is increasingly gaining momentum. New methods and approaches are being formed, cutting across traditional boundaries. Innovative combinations of methods and new developments in techniques allow for deeper insights in fundamental problems and for stronger applications. The Priority Programme will face and accept the challenge to support, promote and organise new collaborations and joint activities of different branches towards solving fundamental problems, developing new methods and applying these methods.
DFG Programme
Priority Programmes
International Connection
Switzerland, USA
Projects
-
Actions of Algebraic Groups, Fans and Tilting Modules
(Applicant
Hille, Lutz
)
-
Affine Nichols algebras of diagonal type and modular tensor categories
(Applicant
Cuntz, Michael
)
-
Algebraic group techniques for finite(ly presented) groups
(Applicant
Plesken, Wilhelm
)
-
Asymptotic branching laws for finite dimensional representations of complex reductive Lie groups by geometric methods
(Applicant
Seppänen, Henrik
)
-
Block Structure, Fusion Systems and Conjectures of Brauer and Olsson
(Applicant
Külshammer, Burkhard
)
-
Branching laws for 1-parameter families of representations of Lie groups and their asymptotic behavior
(Applicant
Hilgert, Joachim
)
-
Classical Yang-Baxter equation and sheaves on degenerations of elliptic curves
(Applicant
Burban, Igor
)
-
Cluster categories and torsion theory
(Applicant
Holm, Thorsten
)
-
Cluster-categories, cluster-tilted algebras and derived equivalences
(Applicant
Holm, Thorsten
)
-
Combinatorial and geometric aspects of the representation theory of finite group schemes
(Applicant
Farnsteiner, Rolf
)
-
Complex geometry of actions and related representations
(Applicant
Heinzner, Peter
)
-
Coordinator project
(Applicant
Littelmann, Peter
)
-
Critical level representations of affine Kac-Moody algebras and the geometric Langlands program
(Applicant
Fiebig, Peter
)
-
Derived categories of sheaves over finite partially ordered sets and their homological properties
(Applicant
Ladkani, Sefi
)
-
Dualities in the representation theory and geometry of loop groups
(Applicant
Fiebig, Peter
)
-
Gabriel-Roiter measure for finite dimensional algebras
(Applicant
Chen, Bo
)
-
Geometry and representation theory in computational complexity
(Applicant
Bürgisser, Peter
)
-
Geometry and the compression of combinatorial formulas for Macdonald polynomals
(Applicant
Littelmann, Peter
)
-
Hermitian symmetric modular category O
(Applicant
Soergel, Wolfgang
)
-
Higher Schur-Weyl dualities and gradings
(Applicant
Stroppel, Catharina
)
-
Homogeneous Einstein metrics and their geometric properties
(Applicant
Agricola, Ilka
)
-
Homological Mirror Symmetry for Singularities
(Applicant
Ebeling, Wolfgang
)
-
Homological structures at the interface of abstract representation theory and algebraic Lie theory
(Applicant
Koenig, Steffen
)
-
Invariant theory of theta-representations
(Applicant
Yakimova, Oksana
)
-
Investigations into the Abelian Defect Group Conjecture
(Applicant
Danz, Susanne
)
-
Investigations on Alperin's Weight Conjecture by means of Auslander-Reiten Quivers
(Applicant
Naehrig, Natalie
)
-
Investigations on the conjectures of McKay and Alperin-McKay
(Applicant
Malle, Gunter
)
-
Koszul duality in representation theory
(Applicant
Soergel, Wolfgang
)
-
Matrix Factorizations and complete Intersection-rings
(Applicant
Burke, Jesse
)
-
Multiplicity Free Actions
(Applicant
Knop, Friedrich
)
-
Non-commutative crepant resolutions and their DT invariants
(Applicant
Mozgovoy, Sergey
)
-
p-adic group rings of finite groups
(Applicant
Nebe, Gabriele
)
-
PBW-filtration of representations, degenerate flag varieties and polytopes
(Applicant
Littelmann, Peter
)
-
Polyhedral models of representation
(Applicant
Bliem, Thomas
)
-
Polyhedral models of representations
(Applicant
Bliem, Thomas
)
-
Positivity in cluster algebras and its relations with categorifications of cluster algebras and total positivity in semisimple algebraic groups
(Applicant
Cerulli Irelli, Giovanni
)
-
Purity of stable pieces in compactifications of semisimple groups
(Applicant
Wedhorn, Torsten
)
-
Quiver moduli and quantized Donaldson-Thomas type invariants
(Applicant
Reineke, Markus
)
-
Quiver representations, singularity categories, and monoidal structures
(Applicant
Krause, Henning
)
-
Recollements and stratifications of derived module categories
(Applicant
Koenig, Steffen
)
-
Representation and category theoretic aspects of logarithmic conformal field theories
(Applicant
Schweigert, Christoph
)
-
Representation theoretic tools for equivariant and orbifold conformal field theories
(Applicant
Schweigert, Christoph
)
-
Representation Theory of the Unitary and Symmetric Group with a view towards the Quantum Marginal Problem
(Applicant
Christandl, Ph.D., Matthias
)
-
Representations of Algebraic Groups in Differential and Difference Galois Theory
(Applicant
Hartmann, Julia
)
-
Restricting Specht Modules of Finite General Linear Groups to the Unitriangular Subgroup
(Applicant
Dipper, Richard
)
-
Semibounded unitary representations of infinite dimensional Lie groups
(Applicant
Neeb, Karl-Hermann
)
-
Serre's notion of complete reducibility and geometric invariant theory
(Applicant
Röhrle, Gerhard
)
-
Shuffles and Schur positivity
(Applicant
Fourier, Ghislain
)
-
Spectral theory of Green functors and other commutative 2-rings
(Applicant
Dell`Ambrogio, Ivo
)
-
Spherical subalgebras of quantized enveloping algebras - structure theory and classification problems
(Applicant
Heckenberger, István
)
-
Structural and geometric study of representations with applications to categorification
(Applicant
Penkov, Ivan
)
-
Structure and representation of cyclotomic Hecke algebras
(Applicant
Malle, Gunter
)
-
The telescope conjecture for derived categories arising in representation theory
(Applicant
Krause, Henning
)
-
Toric structures in derived categories and representations of algebras
(Applicant
Perling, Markus
)