Central charges in Gauged Linear Sigma Models

Gauged Linear Sigma Models (GLSM) are curve-counting theories of a critical locus of a function in a GIT quotient variety. The central part is played by a special matrix factorization on the moduli space of GLSM maps. GLSM invariants satisfy many remarkable properties, many of which are captured by the central charges, that are particular generating series of GLSM invariants that depend on matrix factorizations. In the talk, I will explain what these objects are and how to use central charges to prove symmetry and wall-crossing results for GLSM.