On Certain Lagrangian Subvarieties in Minimal Resolutions of Kleinian Singularities

Seminar: 
Geometry, Symmetry and Physics
Event time: 
Monday, January 27, 2025 - 4:30pm
Location: 
KT 801
Speaker: 
Mengwei Hu
Speaker affiliation: 
Yale
Event description: 

Kleinian singularities are remarkable singular affine surfaces. They arise as quotients of C^2 by finite subgroups of SL_2(C). The exceptional loci in the minimal resolutions of Kleinian singularities are in 1-to-1 correspondence with simply-laced Dynkin diagrams. In this talk, I will introduce certain singular Lagrangian subvarieties in minimal resolutions of Kleinian singularities that appear in the classification of irreducible Harish-Chandra (g, K)-modules. These singular Lagrangian subvarieties have irreducible components given by P^1’s and A^1’s and contain the exceptional locus as a subvariety. I will describe how these irreducible components intersect with each other through the realization of Kleinian singularities as Nakajima quiver varieties.