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VERSION:2.0
PRODID:icalendar-ruby
CALSCALE:GREGORIAN
X-WR-CALNAME:Special Colloquium: : Polytopes\, Ehrhart theory\, matroids\, 
 and beyond...
X-WR-TIMEZONE:Pacific Time (US & Canada)
BEGIN:VEVENT
DTSTAMP:20260820T004655Z
UID:tag:localist.com\,2008:EventInstance_48092155962526
DTSTART:20241122T220000Z
DTEND:20241122T230000Z
DESCRIPTION:Luis Ferroni\, Institute for Advanced Study\n\n\nTitle: Polytop
 es\, Ehrhart theory\, matroids\, and beyond...\n\n\nABSTRACT:\n\nA recurri
 ng idea in combinatorics is to associate with a given combinatorial object
  (say\, a graph\, finite poset\, matroid\, etc.) a convex polytope. Often\
 , the geometric properties of the convex polytope provide insights into th
 e behavior of the object it is derived from. For example\, starting from a
  finite poset P\, one can associate the order polytope of P\, whose normal
 ized volume equals the number of linear extensions of P.\n\n\nIn this talk
 \, we will focus on matroids and explain the natural polytopes associated 
 with them. Rather than concentrating solely on the volume of these polytop
 es\, we will study a more general invariant called the Ehrhart polynomial.
  While this polynomial is exceedingly subtle in the general setting of con
 vex polytopes\, for the special case of matroid polytopes\, certain desira
 ble properties have been established\, while others (long conjectured to h
 old true) have been recently disproved.\n\n\nWe will explore some of the t
 echniques used to tackle these problems on the Ehrhart polynomials of matr
 oids. We will also highlight further generalizations that lead to a system
 atic method for constructing potential counterexamples to other conjecture
 s in matroid theory.
GEO:34.022409;-118.291027
LOCATION:Kaprielian Hall (KAP)\, 414
SUMMARY:Special Colloquium: : Polytopes\, Ehrhart theory\, matroids\, and b
 eyond...
URL;VALUE=URI:https://calendar.usc.edu/event/special-colloquium-polytopes-e
 hrhart-theory-matroids-and-beyond
CATEGORIES:Lecture / Talk / Workshop
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