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URL:/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-alex-fink
SUMMARY:Algebraic and enumerative combinatorics seminar-Alex Fink
CLASS:PUBLIC
DESCRIPTION:Summary \n\nTITLE:The external activity complex of a pair of ma
 troids\n\nSpeaker\n Alex Fink\n\nAffiliation\n Queen Mary University of Lo
 ndon \n\nLocation\n MC 5479\n\nABSTRACT: In 2016\, Ardila and Boocher were
  investigating the variety\nobtained by taking the closure of a linear spa
 ce within A^n in its\ncompactification (P^1)^n\; later work named this the
  \"matroid Schubert\nvariety\". Its Gröbner degenerations led them to def
 ine\, and study the\ncommutative algebra of\, the _external activity compl
 ex_ of a matroid.\nIf the matroid is on n elements\, this is a complex on 
 2n vertices\nwhose facets encode the external activity of bases.\n\nIn rec
 ent work with Andy Berget on Speyer's g-invariant\, we required a\ngeneral
 isation of the definition of external activity where the input\nwas a pair
  of matroids on the same ground set. We generalise many of\nthe results of
  Ardila--Boocher to this setting. Time permitting\, I'll\nalso present the
  tropical intersection theory machinery we use to\nunderstand the external
  activity complex of a pair.\n\nFor those who attended my talk at this yea
 r's CAAC on this paper\, the\ncontent of the present talk is meant to be c
 omplementary.\n\nTHERE WILL BE A PRE-SEMINAR PRESENTING RELEVANT BACKGROUN
 D AT THE\nBEGINNING GRADUATE LEVEL STARTING AT 1:30PM\,\n 
DTSTAMP:20250516T151816Z
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