Algebra Seminar: Bazhanov -- Quantum Dilogarithms and New Integrable Lattice Models in Three Dimension

Vladimir Bazhanov (ANU) will be speaking in the algebra seminar.  We will go out for
lunch after the talk---all are welcome to join! 

When: 12-1pm Friday April 17 

Where: Carslaw 175 

Title: Quantum Dilogarithms and New Integrable Lattice Models in Three Dimension 

Abstract: 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.