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METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20251006T100817Z
DTSTART:20251007T130000Z
DTEND:20251007T140000Z
SUMMARY:Heilbronn Algebra Seminar - Ben Smith
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}gry-mfwf1h3
 d-ttel19
DESCRIPTION:Title: Coxeter matroids\, minuscule varieties and Plücker equ
 ations\n\nAbstract: A matroid is a combinatorial object that can be seen
  as an abstraction of a linear space. For example\, it is defined via a 
 basis exchange relation\, and every linear space gives rise to an underl
 ying matroid. However\, there is a deeper connection via the Grassmannia
 n\, the variety of subspaces of a vector space cut out by the Plücker eq
 uations. Explicitly\, the space of matroids is a ’combinatorial Grassman
 nian’ cut out by the Plücker equations over the Boolean semifield. The p
 rocess that gives these combinatorial equations is called tropicalisatio
 n. Grassmannians and matroids are inherently ’type A’ objects\, and both
  have abstractions associated to other root systems. Grassmannians are p
 articular types of miniscule varieties. As such\, one can generalise to 
 quotients G/P of a simply connected complex Lie group G by a maximal par
 abolic subgroup P with a minuscule fundamental representation. For matro
 ids\, one can generalise to Coxeter matroids whose exchange relations ar
 e governed by different root systems. We generalise the connection betwe
 en these two paradigms to other types\, showing that certain spaces of C
 oxeter matroids are cut out by the tropicalisation of the equations that
  define G/P. (This is joint work with Aram Dermenjian and Alex Fink and 
 Kieran Calvert).
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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