Trent Schirmer will speak on Thursday Sept 11: Title: A lower bound on tunnel number degeneration Abstract: The tunnel t(K) of a knot is given by the equation t(K)+1=g(X), where g(_) denotes Heegaard genus and X is the exterior of K. We prove that t(K#K')\geq \max{t(K),t(K')} for any pair of knots in S^3