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SUMMARY:Robert Berman (Chalmers University of Technology & University of G
 othenburg)
DTSTART:20240508T111500Z
DTEND:20240508T120000Z
DTSTAMP:20260422T155153Z
UID:gbgstats/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/gbgstats/53/
 ">Emergent complex geometry</a>\nby Robert Berman (Chalmers University of 
 Technology & University of Gothenburg) as part of Gothenburg statistics se
 minar\n\nLecture held in MVL14.\n\nAbstract\nA recurrent theme in geometry
  is the quest for canonical metrics on a given manifold X. The prototypica
 l case is when X is a compact orientable two-dimensional surface. Such a m
 anifold can be endowed with a metric of constant curvature\, which is uniq
 uely determined by a fixing a complex structure on X. However\, from a phy
 sical point of view\, geometrical shapes - as we know them from everyday e
 xperience - are\, of course\, not fundamental physical entities. They mere
 ly arise as macroscopic emergent features of ensembles of microscopic poin
 t particles in the limit as the number N of particles tends to infinity. T
 his leads one to wonder if there is a canonical random point process on a 
 given complex manifold X\, from which a canonical metrics emerges as the n
 umber N of points tends to infinity? This is\, indeed\, the case\, when X 
 is a complex algebraic hypersurface of any dimension\, as explained in the
  present talk. In this case the emerging metrics in question have constant
  Ricci curvature. More precisely\, they are Kähler-Einstein metrics. The 
 talk is aimed to be non-technical and no previous background in complex ge
 ometry is required.\n
LOCATION:https://researchseminars.org/talk/gbgstats/53/
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