In 1971, Atiyah and Singer defined an index for certain families of elliptic pseudodifferential operators. In this talk, we construct a C*-algebra of f-continuous operators on $B(L^2M)$, denoted C*(M), defined for any smooth, compact manifold; continuous families of Fredholm operators in C*(M) over a smooth fiber bundle are exactly those with which we can define a families index. Further, the set of these families form another C*-algebra, and the analytic index of each family is equal to their families index.

Bio: Kameron McCombs is an American PhD student at Dartmouth College under Erik van Erp. His research concerns the exploration of a new C*-algebra C*(M) of f-continuous operators, defined for any smooth, compact manifold M. This C*-algebra has applications in index theory related to the families index of Atiyah-Singer.