Schedule

14:00 - 14:30 Kahler geometry and quantization

14:35 - 15:05 Lie 2-groups and quantum gravity

15:10 - 15:40 Lorentz symmetry in quantum field theory

15:40 - 16:00 coffee break

16:00 - 16:30 Algebraic Bethe ansatz for the XXZ Heisenberg spin chain

16:35 - 17:05 Isomonodromic deformations and the Schlesinger system

Venue

Room 1.27 Building 2 Campus de Gambelas

Titles and abstracts

• J. Cidade Mourão

Kahler geometry and quantization

We describe the space of Kahler quantizations of a complex manifold M and its geometry. The geodesic equation is reduced to imaginary time Hamiltonian flows. The lifting of these flows to the quantum bundle leads to generalized coherent state transforms.

• N. Cirilo António

Isomonodromic deformations and the Schlesinger system

Given a linear first order matrix ODE, with rational coefficients, the position of its singularities, in the complex plane, are changed in order to keep the corresponding monodromy data unchanged. Under this deformation the residues of the coefficients act as functions of the positions of the singularities. The corresponding multi-time evolution yields an integrable Hamiltonian system, known as the Schlesinger system.

• A. Miković

Lie 2-groups and quantum gravity

We describe how certain Lie 2-groups can be used for quantization of General Relativity. We explain the role of the Poincare 2-group as well as the role of the Euclidean 2-group.

• R. Potting

Lorentz symmetry in quantum field theory

• I. Salom

Algebraic Bethe ansatz for the XXZ Heisenberg spin chain

We will start with an introduction to the Algebraic Bethe Ansatz. Then we will consider the actual problem of the XXZ spin chain with non-periodic boundary conditions. We will show our results for the corresponding Bethe vectors and explicitly write transfer matrix action on these vectors in the off-shell form. Furthermore, we will discuss certain degrees of freedom for the choice of off-shell solutions, which systematically appear in this context.