Academy of Finland  
Funding decision
Organisation Åbo Akademi University
Project title The six-vertex height field, coupled models, and conformal invariance
Applicant / Contact person Karrila, Alex Mikael
Decision No. 339515
Decision date 03.06.2021
Funding period 01.09.2021 - 31.08.2024
Funding 225 690
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 six-vertex 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 six-vertex model is coupled to various other prominent lattice models. We plan to use recently established new techniques and fundamental results for the six-vertex model to 1) elaborate on the connection of the height field to conformal field theory; 2) use the six-vertex 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.