Eric Rowell, "Braided weakly integral fusion categories"

An important algebraic invariant of fusion categories is the (global) Frobenius-Perron dimension. Of particular interest is the dichotomy between integral and non-integral FP-dimension. There is good evidence to suggest that this (easily determined) dichotomy is related to some key properties of the braid group representations associated with braided fusion categories. I will discuss some conjectures in this vein.