Andrew Elliott

I am a graduate student at Rice University, studying knot theory under Tim Cochran. My specific area of interest is Khovanov homology, and related categorifications. The property of Khovanov homology I have researched is called homological width, which can roughly be thought of as a measure of how much new information Khovanov homology gives over the Jones polynomial.

Preprints

• State Cycles, Quasipositive Modification, and Constructing H-thick Knots in Khovanov Homology
• Graphical methods establishing nontriviality of state cycle Khovanov homology classes

Talks

• Graph-based methods establishing nontriviality of state cycle Khovanov homology classes. AMS Special Session on Geometric Aspects of Link and 3-manifold Invariants, San Francisco, CA. January, 2010.
• Thesis Defense. Rice University. November 17, 2009.
• Graph-based methods establishing nontriviality of state cycle Khovanov homology classes. AMS Special Session on Invariants of Knots and Links, Boca Raton, FL. October 31, 2009.
• Graph-based methods establishing nontriviality of state cycle Khovanov homology classes. LSU Virtual Topology Seminar, Viewed by LSU, U. Iowa, U. Miami, and Rice University. September 9, 2009.
• Construction of H-Thick Knots in Khovanov Homology. AMS Special Session on Link Homology, Washington, DC. January 6, 2009.
• Construction of H-Thick Knots in Khovanov Homology. LSU Virtual Topology Seminar, Viewed by LSU, U. Iowa, U. Miami, Boise State University, and Rice. November 5, 2008
• Construction of H-Thick Knots in Khovanov Homology. AMS Sectional Meeting, Wesleyan, Middleton, CT. October 11, 2008.
• v- State Cycles in Khovanov Homology. Topology Seminar, Rice University, Houston, TX. February 18, 2008.
• Polynomials from Topology. with Peter Horn and Shelly Harvey. Algebraic Geometry: A Conference for Undergraduate Mathematics Majors, Rice University, Houston, TX. Feb 2006.