communication: Counting regions
speaker: Roberto Pagaria (SNS)abstract:
We first discuss a classical problem: how many regions are delimited by some hyperplanes in a real vector space? How many of them are bounded? These numbers depend on how the hyperplanes intersect.
The answers are given by the characteristic polynomial p(x) of the arrangement, i.e. a polynomial associated with the poset of intersections, in particular: # regions=
p(-1)
, # bounded regions=
p(1)
.
In a compact torus we consider a finite set of hypertori and we want to count the number of regions described by these hypertori.
The key point is to consider the poset of connected components of the intersections, instead of the poset of intersections.
In the toric case the number of regions is
p(0)
, the absolute value of the constant term of the characteristic polynomial.
timetable:
Thu 6 Sep, 17:45 - 18:25, Sala Conferenze Centro De Giorgi
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