Area A: Higher structures and (topological) quantum field theories

PIs: Reutter, Schweigert, Wedrich

We investigate partially defined and partially extended 3D and 4D topological field theories determined by higher categories originating in representation theory and link homology theory, with a focus on explicit computability and applications in low-dimensional topology.

PIs: Dyckerhoff, Runkel, Scheimbauer, Schweigert

We plan to investigate higher algebraic structures associated to stratified spaces within the context of topological quantum field theory, aiming to bridge the gap between universal methods and explicit combinatorial approaches.

PIs: Möller, Runkel, Schweigert, Teschner

We investigate relations between 2d CFT and 3d TFT based on non-semisimple categories, with a focus on deformations and derived structures. We explore new links between algebra and geometry, inspired by the reconstruction of vacuum moduli spaces of 3d SUSY QFTs from algebraic structures.

PIs: Runkel, Schomerus

We will advance the quantization of moduli spaces of flat connections at the interface with discrete integrable systems, with focus on compact and non-compact gauge supergroups. Of particular importance are results for conformal (super-)groups which control the bootstrap approach to higher dimensional conformal field theories.