We shall be concerned with the influence of surface geometry on orientational ordering in liquid crystal thin films. We will focus on universal mechanisms, such as merging and splitting of topological defects, reshaping of defect cores, positioning of defects and defect induced global system transformations. All phenomena are analyzed in the frame of 2D or 3D Landau-de Gennes theory in terms of a tensorial order parameter. For the cases studied we discuss future research trends and possible applications.
We first consider possible defect structures and merging of defects in thin nematic shells of various geometries using a 2D approach [1], which has been recently developed by the Pavia group. It is well known [2] that the equilibrium texture of a spherical film exhibits four defects of winding number 1/2 sitting at the vertices of a regular tetrahedron to maximize their mutual distance. By varying the film geometry, the position of the defects and their structure could be altered. Among others things, we show that for sufficiently prolate ellipsoidal shells the four defects merge pairwise at the poles leaving only two +1 defects.
We next consider external field induced transformations of defect cores, positioning of defects, and defect induced or suppressed surface transitions in 3D. For this purpose we consider a hybrid cylindrical cell where we topologically stabilize a boojum in the center of the upper confining plate [3]. If an external electric field is applied, the boojum could be either stretched towards the cell interior or expelled from the cell, depending on the sign of the field anisotropy constant. The stretching of the boojum is also accompanied by a substantial widening of the defect core. Depending on conditions, the presence of the boojum could either substantially increase or depress an external field driven surface biaxial transition.
Finally we consider temperature driven surface wetting and dewetting transitions in a thin film. We show that for appropriate conditions the temperature difference between the surface and bulk phase transition could be anomalously increased with respect to already reported related phenomena.

[1] S. Kralj, R. Rosso, and E. G. Virga, Curvature control of valence on nematic shells, submitted to Soft Matter.
[2] V Vitelli and D. R. Nelson, Nematic textures in spherical shells, Phys. Rev. E 74, 021711 (2006).
[3] S. Kralj, R. Rosso, and E. G. Virga, Finite-size effects on order reconstruction around nematic defects, Phys. Rev. E 81, 021702 (2010).