A new approach to geometric quantization of b-symplectic manifolds

Guillemin, Miranda, and Weitsman introduced a geometric quantization of b-symplectic manifolds (manifolds with symplectic forms with a logarithmic singularity along a hypersurface) that carry a Hamiltonian action of a torus satisfying "quantization commutes with reduction". Braverman, Loizides, and Song, using the Atiyah-Patodi-Singer index, introduced a different approach to the geometric quantization of b-symplectic manifolds with a Hamiltonian action of a compact connected Lie group. In this talk, we discuss a new approach using algebroid-Dirac operators, which were introduced in my previous work with Liu, Loizides, and Sanchez, that addresses a geometric quantization for b-symplectic manifolds with singularities of normal crossing type.