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SUMMARY:Graham Denham (Western University)
DTSTART:20221020T190000Z
DTEND:20221020T200000Z
DTSTAMP:20260423T040216Z
UID:Matroids/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Matroids/6/"
 >Lagrangian Geometry</a>\nby Graham Denham (Western University) as part of
  Matroids - Combinatorics\, Algebra and Geometry Seminar\n\nLecture held i
 n Room 210 The Fields Institute.\n\nAbstract\nIn joint work with Federico 
 Ardila and June Huh\, we introduce the conormal fan of a matroid\, which i
 s an analogue of the Bergman fan.  We use it to give a Lagrangian interpre
 tation of the Chern-Schwartz-MacPherson cycle of a matroid. We also develo
 p tools for tropical Hodge theory to show that the conormal fan satisfies 
 Poincaré duality\, the Hard Lefschetz property\, and the Hodge--Riemann r
 elations.  Together\, these imply conjectures of Brylawski and Dawson abou
 t the log-concavity of the h-vectors of the broken circuit complex and ind
 ependence complex of a matroid.\n
LOCATION:https://researchseminars.org/talk/Matroids/6/
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