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UID:cd823133fc625d79ab86fde0fe0bae2d
CATEGORIES:Joint Princeton-Rutgers Seminar on Geometric PDE's
CREATED:20240311T162005
SUMMARY: Orbifold singularity formation along ancient and immortal Ricci flows
LOCATION:Room 208\, Science & Engineering Resource Center (SEC 208)\, Busch Camp
 us\, Rutgers University
DESCRIPTION: Dimension $4$ is the next horizon for applications of Ricci flow to topolo
 gy, where the main goal is to understand the topological operations that Ri
 cci flow performs both at singular times, and in its long-term behavior. Wi
 th Alix Deruelle, we explain how Ricci flow develops or resolves orbifold s
 ingularities by a notion of stability for orbifold Ricci solitons that we i
 ntroduce depending only on the curvature at the singular points. We constru
 ct ancient and immortal Ricci flows spontaneously forming or desingularizin
 g arbitrarily complicated orbifold singularities by bubbling-off Ricci-flat
  ALE metrics. This unexpectedly predicts that singular spherical and cylind
 rical orbifolds should not appear as finite-time singularity models. On the
  other hand, (complex) hyperbolic orbifolds appear as limits of immortal "t
 hick" $4$-dimensional Ricci flows as $tto+infty$.\n
X-ALT-DESC;FMTTYPE=text/html:<p><strong style="color: #000000; font-family: -webkit-standard; letter-spa
 cing: normal; text-align: left; text-indent: 0px; text-transform: none; whi
 te-space: normal; word-spacing: 0px; text-decoration: none;">&nbsp;</strong
 >Dimension $4$ is the next horizon for applications of Ricci flow to topolo
 gy, where the main goal is to understand the topological operations that Ri
 cci flow performs both at singular times, and in its long-term behavior. Wi
 th Alix Deruelle, we explain how Ricci flow develops or resolves orbifold s
 ingularities by a notion of stability for orbifold Ricci solitons that we i
 ntroduce depending only on the curvature at the singular points. We constru
 ct ancient and immortal Ricci flows spontaneously forming or desingularizin
 g arbitrarily complicated orbifold singularities by bubbling-off Ricci-flat
  ALE metrics. This unexpectedly predicts that singular spherical and cylind
 rical orbifolds should not appear as finite-time singularity models. On the
  other hand, (complex) hyperbolic orbifolds appear as limits of immortal "t
 hick" $4$-dimensional Ricci flows as $tto+infty$.</p>
CONTACT:Tristan Ozuch, MIT
DTSTAMP:20260930T234009
DTSTART;TZID=America/New_York:20240329T153000
DTEND;TZID=America/New_York:20240329T163000
SEQUENCE:0
TRANSP:OPAQUE
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