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DTSTART;TZID=America/Toronto:20260226T143000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-en
 umerative-combinatorics-adrien-segovia-dimension
SUMMARY:Algebraic & Enumerative Combinatorics - Adrien Segovia-The dimensio
 n\nof semidistributive extremal lattices
CLASS:PUBLIC
DESCRIPTION:SPEAKER:\n Adrien Segovia\n\nAFFILIATION:\n Université du Qué
 bec à Montréal\n\nLOCATION:\n MC 5417\n\nABSTRACT: The order dimension 
 of a partially ordered set (poset)\,\nwhich is often difficult to compute\
 , is a measure of its complexity.\nDilworth proved that the dimension of a
  distributive lattice is the\nwidth of its subposet on its join-irreducibl
 e elements. We generalize\nthis result by showing that the dimension of a 
 semidistributive\nextremal lattice is the chromatic number of the compleme
 nt of its\nGalois graph (see Section 3.5 of arXiv:2511.18540). We apply th
 is\nresult to prove that the dimension of the lattice of torsion classes\n
 of a gentle tree with n vertices is equal to n. No advanced background\nis
  required to follow the talk.\n\nThere will be a pre-seminar presenting re
 levant background at the\nbeginning graduate level starting at 1:30pm in M
 C 5417.
DTSTAMP:20260402T155155Z
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