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SUMMARY:Karim Adiprasito (Hebrew University of Jerusalem)
DTSTART:20210209T130000Z
DTEND:20210209T143000Z
DTSTAMP:20260423T022006Z
UID:AGPhy/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AGPhy/6/">Co
 mbinatorics\, Lefschetz theorems beyond positivity and transversality of p
 rimes</a>\nby Karim Adiprasito (Hebrew University of Jerusalem) as part of
  Algebra\, Geometry and Physics seminar (MPIM Bonn/HU Berlin)\n\n\nAbstrac
 t\nI will survey applications of Hodge Theory to combinatorics\, and\, qui
 te suprisingly\, how Hodge-Riemann relations and Lefschetz type theorems c
 an be proven using combinatorial methods\, in settings that are beyond cla
 ssical algebraic geometry\, at least as long as some notion of positivity 
 is available.\n\nI then go one step further\, and ask how many triangles a
  PL embedded simplicial complex in R^4 can have (the answer\, generalizing
  a result of Euler and Descartes\, is at most 4 times the number of edges)
 . I discuss how to reduce this problem to a Lefschetz property beyond proj
 ective structure.\n\nThe main part of the talk is devoted to provide an in
 dication how the proof works\, explain the notion of transversal primes as
  well as Hall matching theorems for spaces of linear operators\, and their
  connection in the Hall-Laman relations which replace our knowledge of the
  signature of the Hodge-Riemann relations in the Kähler case with nondege
 neracy at monomial ideals.\n
LOCATION:https://researchseminars.org/talk/AGPhy/6/
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