University of Sydney Algebra Seminar

Vladimir Bazhanov

Friday 17 April, 12-1pm, in Carslaw 175

Quantum Dilogarithms and New Integrable Lattice Models in Three Dimension

In this talk I will introduce a new class of integrable 3D lattice models, possessing continuous families of commuting layer-to-layer transfer matrices. Algebraically, this commutativity is based on a very special construction of local Boltzmann weights in terms of quantum dilogarithms satisfying the inversion and pentagon identities. The partition function per site in these models can be exactly calculated in the limit of an infinite lattice by using the functional relations, symmetry and factorization properties of the transfer matrix. Remarkably, the integrability conditions in some of these 3D models could also be related with quantization of geometric incidence theorems for three-dimensional circular quadrilateral lattices (lattices whose faces are planar quadrilaterals inscribable into a circle). This talk is based on joint works with Rinat Kashaev, Vladimir Mangazeev and Sergey Sergeev.