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UID:20261109T050932EST-2132T5TX6U@132.216.98.100
DTSTAMP:20261109T100932Z
DESCRIPTION:Title: Pop\, Crackle\, Snap (and Pow): Some Facets of Shards.\n
 \nAbstract: Reading cut the hyperplanes in a real central arrangement H in
 to pieces called shards\, which reflect order-theoretic properties of the 
 arrangement. We show that shards have a natural interpretation as certain 
 generators of the fundamental group of the complement of the complexificat
 ion of H. Taking only positive expressions in these generators yields a ne
 w poset called the pure shard monoid\, which we believe deserves further a
 ttention. When H is simplicial\, its poset of regions is a lattice\, so it
  comes equipped with a pop-stack sorting operator Pop. In this case\, we u
 se Pop to define an embedding Crackle of Reading's shard intersection orde
 r into the pure shard monoid. When H is the reflection arrangement of a fi
 nite Coxeter group\, we also define a poset embedding Snap of the shard in
 tersection order into the positive braid monoid\; in this case\, our three
  maps are related by Snap=Crackle Pop. This talk is based on joint work wi
 th Nathan Williams.\n\n \n\nLocation: 201\, avenue du Président-Kennedy\, 
 PK-4323\, UQAM\, Montréal\n
DTSTART:20221021T150000Z
DTEND:20221021T160000Z
SUMMARY:Colin Defant (MIT)
URL:https://www.mcgill.ca/mathstat/channels/event/colin-defant-mit-342831
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