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SUMMARY:Haotian Wu (The University of Sydney)
DTSTART:20250508T130000Z
DTEND:20250508T140000Z
DTSTAMP:20260404T092651Z
UID:IGTP/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IGTP/
 1/">Asymptotic behavior of unstable perturbations of the Fubini–Study me
 tric in Ricci flow</a>\nby Haotian Wu (The University of Sydney) as part o
 f IUT seminar in Geometry\, Topology and PDE (IGTP)\n\n\nAbstract\nThe Ric
 ci flow can be regarded as a dynamical system on the space of Riemannian m
 etrics. It is important to identify and study its fixed points\, which are
  generalized Einstein metrics known as Ricci solitons. A prominent example
  of a Ricci soliton is the Fubini–Study metric on complex projective spa
 ce. Kröncke has shown that the Fubini–Study metric is an unstable gener
 alized stationary solution of Ricci flow. This raises an interesting quest
 ion: What happens to Ricci flow solutions that start at arbitrarily small 
 but unstable perturbations of the Fubini–Study metric? In a joint work w
 ith Garfinkle\, Isenberg and Knopf\, we carry out numerical simulations wh
 ich indicate Ricci flow solutions originating at unstable perturbations of
  the Fubini–Study metric develop local singularities modeled by the FIK 
 shrinking soliton discovered by Feldman\, Ilmanen and Knopf.\n\nhttps://zo
 om.us/join\nMeeting ID: 836 2536 5334\nPassword: 962501\n\nMeeting ID: 836
  2536 5334\nPassword: 962501\n
LOCATION:https://stable.researchseminars.org/talk/IGTP/1/
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SUMMARY:Panagiotis Gianniotis (The University of Athens)
DTSTART:20250522T133000Z
DTEND:20250522T143000Z
DTSTAMP:20260404T092651Z
UID:IGTP/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/IGTP/
 2/">Splitting maps in Type I Ricci flows</a>\nby Panagiotis Gianniotis (Th
 e University of Athens) as part of IUT seminar in Geometry\, Topology and 
 PDE (IGTP)\n\n\nAbstract\nHarmonic almost splitting maps are an indispensa
 ble tool in the\nstudy of the singularity structure of non-collapsed Ricci
  limit spaces. In\nfact\, by recent work of Cheeger-Jiang-Naber the singul
 ar stratification is\nrectifiable\, and almost splitting maps are used to 
 construct bi-Lipschitz\ncharts of the singular strata. For this\, it is cr
 ucial to understand how a\nsplitting map may degenerate at small scales\, 
 and when it doesn’t.\n\nIn this talk we will discuss similar issues for 
 a parabolic analogue of\nalmost splitting maps\, in the context of the Ric
 ci Flow\, and present some\nnew results regarding the existence and small 
 scale behavior of almost\nsplitting maps in a Ricci flow with Type I curva
 ture bounds. We will also\ndiscuss how these results relate to a conjectur
 e of Perelman on the\nboundedness of the diameter of a 3d Ricci flow devel
 oping a finite time\nsingularity\, as we approach the singular time.\n\nli
 nk: https://meet.google.com/wha-yopd-trc\n
LOCATION:https://stable.researchseminars.org/talk/IGTP/2/
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