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SUMMARY:Victor Reiner (Univerity of Minnesota)
DTSTART:20211118T151500Z
DTEND:20211118T170000Z
DTSTAMP:20260422T065458Z
UID:CJCS/39
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CJCS/39/">To
 pology of augmented Bergman complexes</a>\nby Victor Reiner (Univerity of 
 Minnesota) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nAbst
 ract\n(based on arxiv:2108.13394\; joint with REU students E. Bullock\, A.
  Kelley\, K. Ren\, G. Shemy\, D. Shen\, B. Sun\, A. Tao\, Z. Zhang)\n\nThe
  augmented Bergman complex of a matroid is a simplicial complex introduced
  recently in work of Braden\, Huh\, Matherne\, Proudfoot and Wang. It may 
 be viewed as a hybrid of two well-studied pure shellable simplicial comple
 xes associated to matroids: the independent set complex and the order comp
 lex of the lattice of flats.\n\nAfter recalling the relevance of the augme
 nted Bergman complex in the B-H-M-P-W work\, we show that it is shellable\
 , via two different families of shelling orders. Both shellings determine 
 the homotopy type\, and comparing the two answers re-interprets a known co
 nvolution formula counting bases of the matroid. One of the shellings lead
 s to a surprisingly simple description for how symmetries of the matroid a
 ct on the homology of the complex.\n
LOCATION:https://researchseminars.org/talk/CJCS/39/
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