Monodromy in analytic families of smooth complex surfaces yields groups of isotopy classes of orientation preserving diffeomorphisms for each family member X. For all deformation classes of minimal elliptic surfaces with p g > q = 0, we determine the monodromy group of a representative X, i.e. the group of isometries of the intersection lattice L X := H 2 / torsion generated by the monodromy ac...

The goal of the next two talks is to (1) discuss a class of integrable connections associated to root systems (2) describe their monodromy in terms of quantum groups These connections come in two forms: • Rational form leading to representations of braid groups (this week) • Trigonometric form leading to representations of affine braid groups (next week) The relevance of these connections is th...

In this paper, we give a systematic construction of ten isomonodromic families of connections of rank two on P1 inducing Painlevé equations. The classification of ten families is given by considering the Riemann-Hilbert morphism from a moduli space of connections with certain type of regular and irregular singularities to a corresponding catetorical moduli space of analytic data (i.e., ordinary...

In this talk, we show how the monodromy matrix, M̂, can be constructed for the two dimensional tree level string effective action. The pole structure of M̂ is derived using its factorizability property. It is shown that the monodromy matrix transforms non-trivially under the non-compact T-duality group, which leaves the effective action invariant and this can be used to construct the monodromy ma...

Monodromy groups, i.e. the groups of isometries of the intersection lattice LX := H2/torsion generated by the monodromy action of all deformation families of a given surface, have been computed in [Lö’] for any minimal elliptic surface with pg > q = 0. New and refined methods are now employed to address the cases of minimal elliptic surfaces with pg ≥ q > 0. Thereby we get explicit families suc...