Quantized six-vertex model on a torus

The six-vertex model is arguably the most famous 2D integrable lattice model. Less known is the fact that the model has a 3D origin. In this talk I will discuss the quantization of the six-vertex model, introduced by Kuniba, Matsuike and Yoneyama in 2022 generalizing earlier work of Bazhanov, Mangazeev and Sergeev. The quantized six-vertex model is a 3D integrable lattice model, which has a remarkable property that commuting layer transfer matrices can be defined not only for square lattices but also on more general "admissible" graphs on a torus. Time permitting, I will also explain how the model is related to dimer models, supersymmetric gauge theories and string theory.