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UID:1b54da096afc76d66a79aeb041abfdfc
CATEGORIES:Geometric Analysis Seminar
CREATED:20230417T100152
SUMMARY: 4-dimensional specific aspects of Ricci flows 
LOCATION:HILL 705
DESCRIPTION:Abstract: Ricci flow has been extensively studied, and most results are eit
 her specific to dimension 3 or valid in any dimension. However, given the p
 otential topological applications, a theory specific to the 4-dimensional s
 ituation is desirable. In this discussion, I will present tools and techniq
 ues that are unique to the dimension 4.\n\nTogether with A. Deruelle, we in
 troduce a notion of stability for orbifold singularities. This notion helps
  to explain the formation of orbifold singularities along Ricci flow and le
 ts us construct large classes of ancient Ricci flows. In collaboration with
  K. Naff, we utilize self-duality in dimension 4 to simplify the evolution 
 equations of curvature. Among other things, this approach lets us to uncove
 r intriguing links between Ricci flow and Yang-Mills flow.\n
X-ALT-DESC;FMTTYPE=text/html:<p style="border: 0px; font-style: inherit; font-variant: inherit; font-wei
 ght: inherit; font-size: 15px; line-height: inherit; font-family: inherit; 
 margin: 0px; padding: 0px; vertical-align: baseline; color: inherit;">Abstr
 act: Ricci flow has been extensively studied, and most results are either s
 pecific to dimension 3 or valid in any dimension. However, given the potent
 ial topological applications, a theory specific to the 4-dimensional situat
 ion is desirable. In this discussion, I will present tools and techniques t
 hat are unique to the dimension 4.</p><p style="border: 0px; font-style: in
 herit; font-variant: inherit; font-weight: inherit; font-size: 15px; line-h
 eight: inherit; font-family: inherit; margin: 0px; padding: 0px; vertical-a
 lign: baseline; color: inherit;"><br aria-hidden="true"></p><p>Together wit
 h A. Deruelle, we introduce a notion of stability for orbifold singularitie
 s. This notion helps to explain the formation of orbifold singularities alo
 ng Ricci flow and lets us construct large classes of ancient Ricci flows. I
 n collaboration with K. Naff, we utilize self-duality in dimension 4 to sim
 plify the evolution equations of curvature. Among other things, this approa
 ch lets us to uncover intriguing links between Ricci flow and Yang-Mills fl
 ow.</p>
CONTACT:    SPEAKER: Tristan Ozuch-Meersseman.
DTSTAMP:20260923T015343
DTSTART;TZID=America/New_York:20230418T145000
DTEND;TZID=America/New_York:20230418T155000
SEQUENCE:0
TRANSP:OPAQUE
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