My past research in topology analyzed a class of surfaces, called "incompressible surfaces", in a type of 3-dimensional space that "fibers over the circle". A surface inside a space is called incompressible if any loop in the surface that can be pulled tight in the surrounding space could also be pulled tight without leaving the surface. A 3-dimensional space fibers over the circle if it can be described as a thickened surface with the inside glued to the outside in some theoretical way, even if that gluing can't be accomplished physically within ordinary space. Incompressible surfaces are useful because slicing a space along incompressible surfaces tends to divide the space into simpler pieces.My past research in mathematical modeling of diseases used cost-effectiveness analysis to find the best mammogram screening schedule based on age and risk level and the best risk threshold for offering women at high risk of breast cancer prophylactic treatment with tamoxifen. Although I remain interested in 3-dimensional topology and in mathematical modeling of disease, my current professional focus is on math education and best teaching practices.