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DTSTART:20250309T070000
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DTSTART;TZID=America/Toronto:20251105T143000
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URL:https://uwaterloo.ca/pure-mathematics/events/pure-math-colloquium-58
SUMMARY:Pure Math Colloquium
CLASS:PUBLIC
DESCRIPTION:JOEL KAMNITZER\, MCGILL UNIVERSITY\n\n_The top-heavy conjecture
  and the topology of (real) matroid Schubert\nvarieties_\n\nSuppose we are
  giving a spanning set S in a vector space V and we\nconsider all subspace
 s of V spanned by subsets of S. The top-heavy\nconjecture states that the 
 number of dimension k subspaces is less\nthan or equal to the number for c
 odimension k subspaces. This\nelementary statement was first conjectured b
 y Dowling and Wilson in\n1975 and resisted any proof for 40 years. Finally
  though\, it was\nresolved by Huh and Wang in 2017\, and partially led to 
 Huh's 2022\nFields Medal. I will outline the details of the proof\, which 
 relies on\nthe study of the topology of a beautiful space called a matroid
 \nSchubert variety. Finally\, I will discuss our own contribution to this\
 nsubject\, which is the study of the topology of the real locus of this\ns
 pace (which unfortunately does not lead to the proof of any famous\nconjec
 ture).\n\nMC 5501
DTSTAMP:20260502T041333Z
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