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UID:3ced6ba8-d619-4378-bba9-061cf5fa23d4@nexttoyou
DTSTAMP:20261106T174036Z
DTSTART:20261123T200000Z
DTEND:20261123T210000Z
SUMMARY:Thesis Defense - Michael Law
LOCATION:Building 2 2-146\, 182 MEMORIAL DR\, Cambridge\, MA 02139
DESCRIPTION:Speaker: Michael Law\n\nTitle:\n\nSymmetry\, Stability\, and C
 lassification of Ricci Solitons\n\nAbstract:\n\nRicci solitons provide mo
 dels for singularity formation and resolution in Ricci flow\, while Ricci
 -flat asymptotically locally Euclidean (ALE) spaces arise as local models
  for the degeneration and desingularization of Einstein metrics. In this 
 thesis\, we develop a symmetry principle for steady and expanding gradien
 t Ricci solitons and Ricci-flat ALE spaces under suitable asymptotic cond
 itions. The principle relates symmetries at infinity to global isometries
  through dimension bounds on the kernel of the relevant Lichnerowicz oper
 ator. This kernel measures an obstruction to extending asymptotic symmetr
 ies and is closely connected to linear stability.\n\nWe apply this princi
 ple to characterize the Bryant solitons and the four-dimensional Appleton
  solitons under analytical hypotheses implied by strict stability. For th
 e Appleton characterization\, we also establish uniqueness within Appleto
 n’s defining ansatz and strict stability of the four-dimensional examples
 . More generally\, we classify four-dimensional steady gradient Ricci sol
 itons with vanishing weighted Lichnerowicz kernel that are asymptotically
  cylindrical with link SU(2)/G\, where G is a finite subgroup of SU(2)\, 
 showing that they are quotients of Bryant or Appleton solitons. In the Ri
 cci-flat ALE setting\, bounds on the Lichnerowicz kernel yield characteri
 zations of Eguchi–Hanson space and its higher-dimensional Calabi analo\n\
 nhttp://next-to-u.app/events/3ced6ba8-d619-4378-bba9-061cf5fa23d4
URL:http://next-to-u.app/events/3ced6ba8-d619-4378-bba9-061cf5fa23d4
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