Department of Mathematics - Master Calendar

Abstract: We give an algorithm to reduce the number of generators of the Khovanov chain complex of torus braids (σ1σ2···σn−1)k on n strands. I will begin the talk with context on the stable Khovanov homology of torus links leading to the open question of the structure of their homology theory, as well as potential applications to open questions concerning the colored Jones polynomial. Next I will discuss our work, joint with Carmen Caprau, Nicolle Gonzalez, and Radmila Sazdanovic, using Bar-Natan Gaussian elimination, that gives our whittled complex FTkn. The whittled complex is homotopy-equivalent to the original Khovanov chain complex but with a reduced number of generators. After sketchingthe proof, I will end the talk discussing related future projects.