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SUMMARY:Federico Ardila (San Francisco State University)
DTSTART:20200730T203000Z
DTEND:20200730T220000Z
DTSTAMP:20260423T035712Z
UID:FOTR/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FOTR/21/">La
 grangian Geometry of Matroids</a>\nby Federico Ardila (San Francisco State
  University) as part of Fellowship of the Ring\n\n\nAbstract\nMatroid theo
 ry had its origins in linear algebra and graph theory. In recent years\, t
 he geometric roots of the field have grown much deeper\, bearing many new 
 fruits. The interplay between matroid theory and algebraic geometry has op
 ened up interesting research directions at the intersection of combinatori
 cs\, algebra\, and geometry\, and led to the solution of long-standing que
 stions. \n\nThis talk will discuss my recent joint work with Graham Denham
  and June Huh. We introduce the conormal fan of a matroid M. Inside its Ch
 ow ring\, we find simple interpretations of the Chern-Schwartz-MacPherson 
 cycle of M (a tropical geometric construction) and of the h-vector of M (a
  combinatorial invariant). We then use the Hodge-Riemann relations to prov
 e Brylawski's and Dawson's conjectures that the h-vector of a matroid is l
 og-concave.\n\nI will make the talk as self-contained as possible\, and as
 sume no previous knowledge of matroid theory.\n
LOCATION:https://researchseminars.org/talk/FOTR/21/
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