BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Megan Kerr (Wellesley College)
DTSTART:20210920T140000Z
DTEND:20210920T150000Z
DTSTAMP:20260417T093236Z
UID:CHEM/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CHEM/1/">Hom
 ogeneous Einstein Metrics and Butterflies\, part I</a>\nby Megan Kerr (Wel
 lesley College) as part of Workshop on compact homogeneous Einstein manifo
 lds\n\n\nAbstract\nGiven a compact homogeneous space $G/H$\, we can associ
 ate a "nerve" $X_{G/H}$\, first introduced by M. M. Graev in  2012.\nThe n
 erve $X_{G/H}$ is a purely Lie theoretical compact semi-algebraic set dete
 rmined by the intermediate subgroups $K$ between $H$ and $G$. \n\nTheorem 
 [Gra]\nLet $G/H$ be a compact homogeneous space with $G\,H$ connected. If 
 the nerve $X_{G/H}$ is non-contractible\, then $G/H$\nadmits a $G$-invaria
 nt Einstein metric.\n\n\n The nerve $X_{G/H}$ of a compact homogeneous spa
 ce $G/H$ can be described as follows: To each\nintermediate subalgebra $\\
 mathfrak{k}$  with $\\mathfrak{h}< \\mathfrak{k} <\\mathfrak{g}$ we associ
 ate a (self-adjoint) projection map \n$P$ on $\\mathfrak{g}$ with $P^2=P$ 
 and $\\ker (P)=\\mathfrak{k}$.  Now for each flag $\\varphi = (\\mathfrak{
 k}_1<\\cdots < \\mathfrak{k}_r)$ of non-toral  subalgebras (i.e.\, $\\math
 frak{k}$ is not an abelian extension of $\\mathfrak{h}$)\, we define the s
 implex $\\Delta_\\varphi^P$ as the convex hull of the corresponding projec
 tions on $\\mathfrak{g}$. The nerve $X_{G/H}$ is the union of all such sim
 plices. \nWe will sketch the proof in the nerve $X_{G/H}$ framework.  \n\n
 This is joint work with Christoph Böhm.\n
LOCATION:https://researchseminars.org/talk/CHEM/1/
END:VEVENT
END:VCALENDAR