Workshop on "Algebra and Geometry of Configuration Spaces and related structures" June 21th through 25th
timetable:
Mon 21 Jun, 16:15 - 17:15, Aula Dini
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Lower intervals in the Bruhat order and inversion arrangements
speaker: John Shareshian (Washington University in St. Louis)abstract: Abstract: In joint work with A. Hultman, S. Linusson and J. Sj\"ostrand, we proved the following conjecture of A. Postnikov. Let w be an element of the symmetric group Sn. Let Aw be the arrangement of those hyperplanes in Rn defined by the equations xi=xj whenever (i,j) is an inversion of w. Then
(1) The number of regions in the complement of Aw is at most the number of elements below w in the Bruhat order, and
(2) equality holds in (1) if and only if w avoids a fixed (finite and known) set of patterns.
I will describe in some detail our proof of (1), which works for any finite Coxeter group. I will discuss some aspects of (2) if time permits.
timetable:
Mon 21 Jun, 16:15 - 17:15, Aula Dini
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