Central charges of B-branes at non geometric phases

Abstract: I'll give an overview of basic concepts about B-branes and their central charges and how they arise in physics and mathematics. In particular I'll present the gauge linear model approach which allows for defining quantities in the full stringy Kahler moduli M of certain Calabi-Yaus (CY). Then, I'll show some examples and motivate an intrinsic definition of the central charges on phases (some sub-regions of M), based on field theory data. I'll put particular emphasis on Landau-Ginzburg (orbifold) phases of CY hypersurfaces and comparison with results in FJRW theory. If time allows I'll comment on applications to not complete intersections and non-CY cases.