Speaker: Jozef Przytycki, GWU

http://home.gwu.edu/~przytyck/

Place: Monroe Hall (2115 G Street), Room 267

Title: Curtain homology and logic

Abstract: We show a simple visualization that allows us to construct homology theory for a Yang-Baxter operator. The linear map $R: V\otimes V \to V\otimes V$ is called by Fadeev school of theoretical physics the Yang-Baxter operator if it is invertible and satisfies the following equation:
$(R\otimes Id) (Id \otimes R)(R\otimes Id) = (Id \otimes R)(R\otimes Id)(Id \otimes R)$.
We show that the quandle homology, in its cubic form, can be presented graphically using a diagram (curtain diagram). This in turn gives rise to homology of Yang-Baxter operator. We speculate that this homology is related to Khovanov homology of links and gives a deep connection between Knot Theory and Statistical Physics.