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BEGIN:VEVENT
SUMMARY:Megan Kerr (Wellesley College)
DTSTART:20210920T140000Z
DTEND:20210920T150000Z
DTSTAMP:20260415T054833Z
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
BEGIN:VEVENT
SUMMARY:Wolfgang Ziller (UPenn)
DTSTART:20210921T140000Z
DTEND:20210921T150000Z
DTSTAMP:20260415T054833Z
UID:CHEM/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CHEM/2/">On 
 the Palais-Smale condition for the prescribed Ricci curvature functional a
 nd the existence of saddle points</a>\nby Wolfgang Ziller (UPenn) as part 
 of Workshop on compact homogeneous Einstein manifolds\n\n\nAbstract\nGiven
  a metric $T$\, we want to solve the\nequation $Ric(g)=cT$ for a metric $g
 $ (and a constant $c$). It is well known that they are critical points of 
 the scalar curvature $Scal$ under the constraint $\\operatorname{tr}_gT=1$
 . We study this problem in the case of homogeneous spaces $G/H$. For the c
 orresponding\nproblem for Einstein metrics it was shown that $Scal$ satisf
 ies the Palais-Smale condition\, which gives rise to a large class of Eins
 tein metrics which are saddle points of the functional. We will discuss th
 is condition in our case and will see that Palais-Smale  is not satisfied\
 , and how one can nevertheless use a mountain pass type argument to produc
 e saddle points. This is joint work with Artem Pulemotov.\n
LOCATION:https://researchseminars.org/talk/CHEM/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Arvanitoyeorgos (Univ. Patras)
DTSTART:20210922T140000Z
DTEND:20210922T150000Z
DTSTAMP:20260415T054833Z
UID:CHEM/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CHEM/3/">Ein
 stein metrics on Stiefel manifolds and compact Lie groups</a>\nby Andreas 
 Arvanitoyeorgos (Univ. Patras) as part of Workshop on compact homogeneous 
 Einstein manifolds\n\n\nAbstract\nI will review old and new results about 
 $G$-invariant Einstein metrics on real\, complex and quaternionic Stiefel 
 manifolds $G/H = {V}_{k}\\mathbb{F}^{n}$ $(\\mathbb{F} = \\mathbb{R}\, \\m
 athbb{C}$  or $\\mathbb{H})$ and left-invariant Einstein metrics on compac
 t\nsimple Lie groups\, which are not naturally reductive.\n\nThe presentat
 ion is based on joint works with Yusuke Sakane and Marina Statha.\n
LOCATION:https://researchseminars.org/talk/CHEM/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stavros Anastassiou (Univ. Patras)
DTSTART:20210922T150000Z
DTEND:20210922T160000Z
DTSTAMP:20260415T054833Z
UID:CHEM/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CHEM/4/">Glo
 bal study of the Ricci flow on flag manifolds with second Betti number equ
 al to 1</a>\nby Stavros Anastassiou (Univ. Patras) as part of Workshop on 
 compact homogeneous Einstein manifolds\n\n\nAbstract\nFor any flag manifol
 d $M = G/K$ of a compact simple Lie group $G$ we describe some qualitative
  properties of the homogeneous un-normalized Ricci flow. We engage ourselv
 es with the global study of the dynamical system induced by this flow on a
 ny flag manifold $M = G/K$ with second Betti number $b_2(M) = 1$\, and pre
 sent non-collapsed ancient solutions\, whose $\\alpha$-limit set consists 
 of fixed points at infinity of $\\mathscr{M}^G$ . Based on the Poincaré c
 ompactification method\, we show that these fixed points correspond to inv
 ariant Einstein metrics\, which we classify according to their stability p
 roperties\, illuminating thus the structure of the system¢s phase space. 
 This is a joint work with Ioannis Chrysikos.\n
LOCATION:https://researchseminars.org/talk/CHEM/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrzej Derdzinski (Ohio State Univ.)
DTSTART:20210923T140000Z
DTEND:20210923T150000Z
DTSTAMP:20260415T054833Z
UID:CHEM/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CHEM/5/">Cur
 vature-homogeneous pseudo-Riemannian Einstein four-manifolds</a>\nby Andrz
 ej Derdzinski (Ohio State Univ.) as part of Workshop on compact homogeneou
 s Einstein manifolds\n\n\nAbstract\nIn the Riemannian case they are all lo
 cally homogeneous (and hence locally\nsymmetric due to a 1969 result of Je
 nsen). By contrast\, for the neutral sign\npattern $(- - + +)$\, simple ex
 amples show that the local-isometry types of\ncurvature-homogeneous Ricci-
 flat metrics form an in finite-dimensional moduli\nspace (and so "most" of
  them are not locally homogeneous). In the Lorentzian\nsignature\, the sam
 e phenomenon arises as a consequence of Brans's 1971\nclassification of Pe
 trov type III metrics. The talk presents local-structure\ntheorems for som
 e special classes of such four-manifolds.\n
LOCATION:https://researchseminars.org/talk/CHEM/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lino Grama (Univ. Campinas)
DTSTART:20210924T140000Z
DTEND:20210924T150000Z
DTSTAMP:20260415T054833Z
UID:CHEM/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CHEM/6/">Pro
 jected Ricci flow and applications to flag manifolds</a>\nby Lino Grama (U
 niv. Campinas) as part of Workshop on compact homogeneous Einstein manifol
 ds\n\n\nAbstract\nIn this talk we will present a normalization for the hom
 ogeneous Ricci flow with natural compactness properties. Our method consis
 ts in appropriately normalizing the flow to a simplex and time reparametri
 zing it to get polynomial equations\, obtaining what we call the "projecte
 d Ricci flow". As an application\, we present a detailed picture of the ho
 mogeneous Ricci flow for three isotropy-summands flag manifolds: phase por
 traits\, basins of attractions\, conjugation classes and collapsing phenom
 ena. This is a joint work with R. M. Martins\, M. Patrão\, L. Seco\, and 
 L. D. Sperança.\n
LOCATION:https://researchseminars.org/talk/CHEM/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:McKenzie Wang (McMaster Univ.)
DTSTART:20210927T140000Z
DTEND:20210927T150000Z
DTSTAMP:20260415T054833Z
UID:CHEM/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CHEM/7/">The
  linear stability of some families of Einstein manifolds</a>\nby McKenzie 
 Wang (McMaster Univ.) as part of Workshop on compact homogeneous Einstein 
 manifolds\n\n\nAbstract\nI will motivate and describe some joint work with
  Uwe Semmelmann and Changliang Wang\n regarding the linear stability of ma
 nifolds which admit a non-trivial real Killing spinor.\n
LOCATION:https://researchseminars.org/talk/CHEM/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Böhm (Univ. Muenster)
DTSTART:20210928T140000Z
DTEND:20210928T150000Z
DTSTAMP:20260415T054833Z
UID:CHEM/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CHEM/8/">Hom
 ogeneous Einstein Metrics and Butterflies\, part II</a>\nby Christoph Böh
 m (Univ. Muenster) as part of Workshop on compact homogeneous Einstein man
 ifolds\n\n\nAbstract\nWe will present applications of the Nerve Theorem an
 d the  Simplex Theorem\, and discuss open questions.\n\nThis is joint work
  with Megan Kerr.\n
LOCATION:https://researchseminars.org/talk/CHEM/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Pope (Texas A&M Univ.)
DTSTART:20210930T140000Z
DTEND:20210930T150000Z
DTSTAMP:20260415T054833Z
UID:CHEM/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CHEM/9/">Hom
 ogeneous Einstein Metrics\, Supersymmetry and Pseudo-Supersymmetry</a>\nby
  Christopher Pope (Texas A&M Univ.) as part of Workshop on compact homogen
 eous Einstein manifolds\n\n\nAbstract\nCompact Einstein spaces have been o
 f interest for Kaluza-Klein reduction of higher-dimensional supergravity t
 heories since the 1980s. One of the earliest "exotic" applications was the
  reduction of eleven-dimensional supergravity on the Jensen squashed 7-sph
 ere\, giving a four-dimensional theory with N=1 supersymmetry.  Compact se
 mi-simple group manifolds can provide large classes of homogeneous squashe
 d Einstein metrics\, with increasing richness as the dimension increases. 
  Most of these lie beyond the range of dimensions relevant for ordinary su
 pergravities\, which exist only in eleven dimensions or less.  However\, i
 f certain of the requirements for strict supersymmetry are relaxed\, theor
 ies with "pseudo-supersymmetry" can be constructed in arbitrary dimensions
 \, and these provide a framework within which group manifold compactificat
 ions may have interesting applications.\n
LOCATION:https://researchseminars.org/talk/CHEM/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emilio Lauret (Univ. Nac. del Sur)
DTSTART:20210929T140000Z
DTEND:20210929T150000Z
DTSTAMP:20260415T054833Z
UID:CHEM/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CHEM/10/">On
  the stability of homogeneous standard Einstein manifolds</a>\nby Emilio L
 auret (Univ. Nac. del Sur) as part of Workshop on compact homogeneous Eins
 tein manifolds\n\n\nAbstract\nWe will study the stability type of compact 
 homogeneous Einstein manifolds as critical points of the normalized total 
 scalar curvature functional. \nWe will focus on standard Einstein manifold
 s $G/K$ with $G$ simple\, which were classified by Wang and Ziller. \n\n\n
 This is work in progress in collaboration with Jorge Lauret.\n
LOCATION:https://researchseminars.org/talk/CHEM/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yurii Nikonorov (Vladikavkaz Centre)
DTSTART:20211001T140000Z
DTEND:20211001T150000Z
DTSTAMP:20260415T054833Z
UID:CHEM/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CHEM/11/">Th
 ree topics on compact homogeneous Einstein manifolds</a>\nby Yurii Nikonor
 ov (Vladikavkaz Centre) as part of Workshop on compact homogeneous Einstei
 n manifolds\n\n\nAbstract\nThis talk consists of three parts. In the first
  part\, we discuss how to use distinct Lie groups transitive on a given co
 mpact manifold $M$ to study of invariant Einstein metrics on $M$. The seco
 nd topic is devoted to the classification of compact homogeneous Einstein 
 manifolds in low dimensions. In the last part\, we consider some examples 
 of compact homogeneous spaces with a large number of invariant Einstein me
 trics.\n
LOCATION:https://researchseminars.org/talk/CHEM/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yusuke Sakane (Osaka Univ.)
DTSTART:20210929T130000Z
DTEND:20210929T140000Z
DTSTAMP:20260415T054833Z
UID:CHEM/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CHEM/12/">Ex
 istence and non-existence of Einstein metrics  on compact homogeneous  man
 ifolds</a>\nby Yusuke Sakane (Osaka Univ.) as part of Workshop on compact 
 homogeneous Einstein manifolds\n\n\nAbstract\nWe discuss existence and non
 -existence of Einstein metrics on  certain compact homogeneous manifolds $
 G/H$. \nStudy of existence and  non-existence of Einstein metrics  on $G/H
 $ is started by Wang and Ziller in 1986.   Park and speaker  studied some 
 spaces $G/H$ with three irreducible summands in 1997\,  and more general r
 esults for non-existence are obtained by  Böhm in 2005. In 2008\, Dickins
 on and Kerr studied existence and non-existence of Einstein metrics on $G/
 H$ with two irreducible summands. \n\nOne of the results of Böhm is that 
 compact homogeneous manifolds $G/H = SU(n+k_1+ \\cdots +k_p)/S(SO(n)U(1)\\
 times U(k_1) \\times\\cdots\\times U(k_p))$ (where $SO(n)U(1) \\subset U(n
 ) $) does not admit $G$-invariant Einstein metrics\,  if $n > (k_1+\\cdots
 +k_p)^2+2$. He has obtained the results by considering ``traceless" part o
 f Ricci tensor.  \n\nWe can apply his method for other compact homogeneous
  manifolds $G/H$.  \n\n1) For $G/H = Sp(n+k_1+ \\cdots +k_p)/SO(n)Sp(1)\\t
 imes Sp(k_1) \\times\\cdots\\times Sp(k_p)$ \n(where $SO(n)Sp(1) \\subset 
 Sp(n)$)\,  if $n \\geq  6 (k_1+\\cdots+k_p)$ ($k_i \\geq  1$)\, then \n$G/
 H$ does not admit $G$-invariant Einstein metrics\n\n2) For $G/H = SO(4 n+k
 _1+ \\cdots +k_p)/Sp(n)Sp(1)\\times SO(k_1) \\times\\cdots\\times SO(k_p)$
  \n(where $Sp(n)Sp(1) \\subset SO(4n)$)\, if  $n \\geq  (3/2)( k_1+ \\cdot
 s +k_p)$ ($k_i \\geq 3$)\, then $G/H$ does not admit $G$-invariant Einstei
 n metrics. \n\nFor \n$G/H = SO(2 n+k_1+ \\cdots +k_p)/ SO(n)U(1)\\times SO
 (k_1) \\times\\cdots\\times SO(k_p)$ (where $SO(n)U(1) \\subset U(n) \\sub
 set SO(2 n)$)\, we can not  apply the method directly. In this talk\, we w
 ill show that\, if $n \\geq 5 (k_1+ \\cdots +k_p)$ ($k_i \\geq 3$)\, $G/H$
  does not admit $G$-invariant Einstein metrics  by modifying argument of  
 ``traceless" part of Ricci tensor. \n\nFor existence of Einstein metrics\,
  in general\, it is difficult for compact homogeneous manifolds $G/H$ abov
 e.\n But\, in case of $ k_1 = \\cdots = k_p=k $\, we see that\, for a  giv
 en $p \\geq 1$ there exists a pair \n$(n\, k)$ such that  $G/H$ admits at 
 least two  $G$-invariant Einstein metrics.\n
LOCATION:https://researchseminars.org/talk/CHEM/12/
END:VEVENT
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