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DTSTART:20220313T070000
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DTSTART;TZID=America/Toronto:20230302T143000
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URL:https://uwaterloo.ca/pure-mathematics-geometry-topology/events/homotopi
 cal-obstructions-existence-certain-complex
SUMMARY:Homotopical obstructions to the existence of certain complex\nstruc
 tures on smooth manifolds
CLASS:PUBLIC
DESCRIPTION:SCOTT WILSON\, CITY UNIVERSITY OF NEW YORK\n\nA difficult open 
 problem is to determine if there are topological\nobstructions to complex 
 structures on smooth manifolds (of even\ndimension greater than or equal t
 o six) beyond the fairly\nwell-understood obstructions to almost complex s
 tructures.  In this\ntalk\, I will explain that certain types of complex
  structures are\nhomotopically obstructed in these dimensions\, where the 
 “types”\nare organized by the structure of the underlying bicomplex of
 \ndifferential forms.  To establish this\, I’ll describe some\nnumeric
 al inequalities for complex manifolds of the form “Topology\nis less tha
 n or equal to Complex-analysis”. The topology invariants\nroughly measur
 e the failure of the algebra of differential forms to be\nequivalent to it
 s cohomology\, and the complex-analytic invariants\nmeasure the “wildnes
 s” of the bi-complex of differential forms.\nExplicit examples will be g
 iven. This is joint work with Jonas\nStelzig.\n\nMC 5417
DTSTAMP:20260311T211650Z
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