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SUMMARY:Martin de Borbon (Université de Nantes)
DTSTART:20200709T120000Z
DTEND:20200709T133000Z
DTSTAMP:20260422T225844Z
UID:MathsSeminaratSH/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MathsSeminar
 atSH/1/">Calabi-Yau metrics with cone singularities along intersecting com
 plex lines: The unstable case</a>\nby Martin de Borbon (Université de Nan
 tes) as part of Maths Seminar at Shanghai\n\n\nAbstract\nAbstract: In coll
 aboration with G. Edwards we produce (local) Calabi-Yau metrics\, in two c
 omplex dimensions\, with cone singularities along intersecting complex lin
 es\, for cone angles that strictly violate the Troyanov condition. We iden
 tify the tangent cone at the origin as a product of two 2-cones. In the ta
 ngent cone limit\, the line with the smallest cone angle remains apart whi
 le the other lines collide into a single cone factor. \n\nTo prove our res
 ult\, we first write an approximate solution with the desired asymptotic b
 ehavior and small Ricci potential. The main difficulty is to invert the La
 placian of such approximate solution metric in suitable Holder spaces. Onc
 e this is done\, we use the implicit function theorem to perturb into an a
 ctual Calabi-Yau metric.\n
LOCATION:https://researchseminars.org/talk/MathsSeminaratSH/1/
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SUMMARY:Jian Wang (Universität Augsburg)
DTSTART:20200826T120000Z
DTEND:20200826T140000Z
DTSTAMP:20260422T225844Z
UID:MathsSeminaratSH/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MathsSeminar
 atSH/2/">Topology of 3-manifolds with uniformly positive scalar curvature<
 /a>\nby Jian Wang (Universität Augsburg) as part of Maths Seminar at Shan
 ghai\n\n\nAbstract\nAbstract: One of fundamental questions is  how to clas
 sify open 3-manifolds with positive scalar curvature. The topology of open
  3-manifolds is much complicated. For example\, Geometrization conjecture 
 is failed to be generalized to open 3-manifolds. In this talk\, we give a 
 classification for open 3-manifolds with uniformly positive scalar curvatu
 re. Precisely\, we use minimal surface theory to give a prime decompositio
 n for such manifolds.\n\nZoom Meeting\nPlease register in advance for thes
 e meetings.\nAfter registration\, you will receive a confirmation email co
 ntaining information about joining the meetings.\n
LOCATION:https://researchseminars.org/talk/MathsSeminaratSH/2/
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BEGIN:VEVENT
SUMMARY:Yu Li (Stony Brook University)
DTSTART:20200827T130000Z
DTEND:20200827T150000Z
DTSTAMP:20260422T225844Z
UID:MathsSeminaratSH/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MathsSeminar
 atSH/3/">Singularity models of the Ricci flow</a>\nby Yu Li (Stony Brook U
 niversity) as part of Maths Seminar at Shanghai\n\n\nAbstract\nAncient sol
 utions model the singularity formation of the Ricci flow.  In two and thre
 e dimensions\, we currently have complete classifications for κ-noncollap
 sed ancient solutions\, while the higher dimensional problem remains open.
  This talk will survey recent developments of Ricci shrinkers\, which form
  an important class of ancient solutions\, and higher dimensional ancient 
 solutions.\n
LOCATION:https://researchseminars.org/talk/MathsSeminaratSH/3/
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BEGIN:VEVENT
SUMMARY:Zakarias Sjöström Dyrefelt (ICTP Trieste)
DTSTART:20200825T130000Z
DTEND:20200825T150000Z
DTSTAMP:20260422T225844Z
UID:MathsSeminaratSH/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MathsSeminar
 atSH/4/">Optimal lower bounds for the J-functional and applications to exi
 stence of cscK metrics</a>\nby Zakarias Sjöström Dyrefelt (ICTP Trieste)
  as part of Maths Seminar at Shanghai\n\n\nAbstract\nExistence of constant
  scalar curvature Kähler (cscK) metrics on compact Kähler manifolds is a
  central question in complex geometry. Following the variational approach 
 pioneered by Mabuchi in the 1980's it was recently proven (by X.X. Chen an
 d J. Cheng) that existence of cscK metrics is equivalent to coercivity of 
 the Mabuchi K-energy functional on the space of Kähler metrics. In this t
 alk I will present new coercivity estimates directly related to this probl
 em\, focusing on the strongly related J-functional of Chen/Donaldson\, whi
 ch occurs as the “energy part” in the Chen-Tian decomposition of the K
 -energy\, and whose Euler-Lagrange equation is Donaldson’s J-equation.\n
 \nAs a main result of the talk we give an explicit and optimal lower bound
  for the J-functional\, in the sense of finding the largest possible const
 ant in the definition of coercivity (which always exists and takes negativ
 e values in general). This has applications to stability\, and sheds new l
 ight on existence criteria for cscK metrics using Tian's alpha invariant\,
  in the spirit of Dervan and Li-Shi-Yao. As a third application we explain
  that there must always exist cscK metrics on compact Kähler manifolds wi
 th nef canonical bundle\, thus on all smooth minimal models\, and also on 
 the blowup of any such manifold. This extends a result of Jian-Shi-Song wi
 th a proof that does not depend on the Abundance conjecture.\n
LOCATION:https://researchseminars.org/talk/MathsSeminaratSH/4/
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