Speaker: Song Gao
University of Notre Dame
Will give a PhD Defense entitled:
COISOTROPICITY OF FIXED POINTS UNDER TORUS ACTION ON THE VARIETY OF LAGRANGIAN SUBALGEBRAS
Abstract: Let g be a complex semi-simple Lie algebra with adjoint group G. Consider the standard Manin triple structure on the double Lie algebra d := g ⊕ g and the associated variety of Lagrangian subalgebras L(d). In this thesis, we study the variety CL(d) of coisotropic subalgebras of g, which is embedded as a subvariety of L(d). The diagonal maximal torus H∆ in G × G acts on L(d) and CL(d). We describe the connected components of the fixed point set L(d)H∆ using toric varieties, and we compute the irreducible components of the fixed point set CL(d)H∆. We provide the first examples of continuous families in CL(d)H∆. Our results may be viewed as completing and unifying the earlier works of Zambon, Kroeger and Le.
Date: 06-27-2024
Time: 8:00 am
Location: Zoom NA
Zoom URL: notredame.zoom.us/j/