University of California, Santa Barbara, Department of Mathematics
The focus of my graduate studies is 3-manifold topology with an emphasis on Heegaard splittings.
A Heegaard splitting is a method of decomposing a 3-manifold into two simpler pieces.
All 3-manifolds admit a Heegaard splitting and these splittings can provide information about the topology of the original 3-manifold.
One such property of a Heegaard splitting is its "distance," which roughly measures the complexity of the Heegaard splitting.
My dissertation focuses on the relationship between the gluing map between two handlebodies and the resulting distance of the Heegaard splitting.
In particular, I showed how distance is affected when using Dehn twists (a twist of the surface about a curve) as the gluing map.
You can check out slides from my recent talk at the Joint Mathematics Meetings here for more information (and pictures!).