Students

Nancy Scherich VIGRE funded REU summer project, 2010.
This project studied basic knot theory and knot invariants by way of grid diagrams. Scherich's article A simplification of grid equivalence (submitted to Topology and its Applications) proves that of the three possible moves for grid equivalence, one move is a consequence of the other two.

Yu Li CSST program research project, 2011.
This project studied the fundamental groups of 3-manifolds admitting a genus one open book decomposition with a single boundary component. Our joint paper Genus one open books with non-left-orderable fundamental group (to appear in Proceedings of the AMS) proves that L-space implies non-left-orderable fundamental group for this class of manifolds.

Jose Chavez UC Leads research project, 2011.
This project studied the state sum formula for the Jones polynomial, and Khovanov homology. Chavez presented a poster on his work at the 2011 SACNAS meeting in San Jose.

Jeff Hicks VIGRE funded REU summer project (ongoing), 2012.
This ongoing project focusses on Khovanov homology, with emphasis on a particular variant of the theory due to Bar-Natan. Hicks extends results of Turner and establishes an equivalence between Bar-Natan's module and a related filtered knot homology (in the sense of Rasmussen) in his article-in-preparation Modules and filtrations in Khovanov homology.

Isaac Solomon VIGRE funded REU summer project (ongoing), 2012.
This ongoing project focusses on left-orderable groups in topology, with emphasis on the conjectured relationship between L-spaces and manifolds with non-left-orderable fundamental group. Solomon is currently studying and expanding on examples of decayed knots.

                                                                                [back]