Dear Topologists and Friends of Topology,
     Trent will give the first seminar talk of the semester tomorrow (Thursday) at 3:30 in MSCS 514. Title and abstract are below:

Title: Lower bounds on the Heegaard genus of amalgamated $3$-manifolds.

Abstract: I describe some new results of mine which place lower bounds on the Heegaard genus of a $3$-manifold which is obtained by gluing two $3$-manifolds together along torus boundary components. As an application, I also put a lower bound on tunnel number degeneration under connected sum of knots. These kinds of problem have been worked on for quite some time, but as far as I know my techniques are new and the results are of a different flavor.