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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-alex-fink
SUMMARY:Algebraic and enumerative combinatorics seminar-Alex Fink
CLASS:PUBLIC
DESCRIPTION:TITLE:The external activity complex of a pair of matroids\n\nSp
 eaker\n Alex Fink\n\nAffiliation\n Queen Mary University of London \n\nLoc
 ation\n MC 5479\n\nABSTRACT: In 2016\, Ardila and Boocher were investigati
 ng the variety\nobtained by taking the closure of a linear space within A^
 n in its\ncompactification (P^1)^n\; later work named this the \"matroid S
 chubert\nvariety\". Its Gröbner degenerations led them to define\, and st
 udy the\ncommutative algebra of\, the _external activity complex_ of a mat
 roid.\nIf the matroid is on n elements\, this is a complex on 2n vertices\
 nwhose facets encode the external activity of bases.\n\nIn recent work wit
 h Andy Berget on Speyer's g-invariant\, we required a\ngeneralisation of t
 he 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--Boo
 cher to this setting. Time permitting\, I'll\nalso present the tropical in
 tersection theory machinery we use to\nunderstand the external activity co
 mplex of a pair.\n\nFor those who attended my talk at this year's CAAC on 
 this paper\, the\ncontent of the present talk is meant to be complementary
 .\n\nTHERE WILL BE A PRE-SEMINAR PRESENTING RELEVANT BACKGROUND AT THE\nBE
 GINNING GRADUATE LEVEL STARTING AT 1:30PM\,
DTSTAMP:20260403T081805Z
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