On the first half of my talk, I'll focus on 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 setting which allows for defining quantities in full stringy Kahler moduli of certain Calabi-Yaus (CY). In the second half I'll show some examples and motivate an intrinsic definition of the central charges, 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. Speaker(s): Mauricio Romo (IAS)