Project description 
This project is in the intersection of mathematical physics and probability, studying the connection of random models on planar lattices and conformally invariant quantum field theories (CFTs). We approach this connection via the sixvertex model, a classical model for the random crystalline structure of water ice. On the one hand, it has a random field representation, conjecturally connecting it to the CFT, and a random geometry representation, connecting it to a wealth of recent mathematical
literature. On the other hand, the sixvertex model is coupled to various other prominent lattice models. We plan to use recently established new techniques and fundamental results for the sixvertex model to
1) elaborate on the connection of the height field to conformal field theory;
2) use the sixvertex model as a unified framework to prove properties for the coupled random models; and
3) elaborate on the connection of the random geometry and fields approaches. 
