In this talk, I will describe a systematic approach for extending a class of integro-differential operators, defined on hypersurfaces, to ones defined in the tubular neighborhoods in the ambient Euclidean space. Surface integrals become volume integrals with identical evaluations. Such extensions facilitate the development of numerical methods for boundary integral methods and partial differential equations in applications where parameterization of surfaces is costly or difficult (e.g. inverse problems involving shapes). I will show applications of the implicit boundary integral method and relate to other existing methods. Speaker(s): Richard Tsai (University of Texas, Austin)