Abstract: Kleinian singularities are quotients of C^2 by finite subgroups of SL_2(C). They are in bijection with the ADE Dynkin diagrams via the McKay correspondence. In this talk, I will introduce certain singular Lagrangian subvarieties in the minimal resolutions of Kleinian singularities, motivated by the geometric classification of unipotent Harish-Chandra (g,K)-modules. The irreducible components of these singular Lagrangian subvarieties are P^1’s and A^1’s. I will describe how they intersect with each other through the realization of Kleinian singularities as Nakajima quiver varieties. I will also discuss their connections with nilpotent K-orbits and symmetric pairs in semisimple Lie algebras.

The defense will be preceeded by special tea at 3.30 in the lounge.