[Binghamton Geometry/Topology Seminar] Geometry/Topology Seminar this Thursday

[Tam Nguyen Phan]

  BINGHAMTON GEOMETRY/TOPOLOGY SEMINAR


   Date: Thursday, September 10th, 2015

   Time:  2.50 pm

   Place: Whitney Hall, Room 100E,  followed by coffee/tea in the
      Hilton Reading Room. Note the new location of the math department (
http://www2.math.binghamton.edu/p/directions).


   Speaker: Wiktor Mogilski (Binghamton University)

   Title:  The weighted Singer conjecture for Coxeter groups

    Abstract: Associated to a Coxeter system (W,S) there is a contractible
simplicial complex Sigma called the Davis complex on which W acts properly
and cocompactly by reflections. Given an S-tuple of positive real numbers q,
one can define the weighted L^2-(co)homology groups of Sigma and associate
to them a nonnegative real number called the weighted L^2-Betti number.
Within the spectrum of weighted L^2-(co)homology there is a conjecture of
interest called the Weighted Singer Conjecture, which was formulated in a
2007 paper of Davis--Dymara--Januszkiewicz--Okun. The conjecture claims
that if Sigma is an n-manifold, then the weighted L^2-(co)homology groups
of Sigma vanish above dimension n/2 whenever q\leq\1 (that is, all terms of
the multiparameter q are less than or equal to 1). I will provide an
overview of the current progress on the conjecture and present proofs of
the conjecture (and variations of it) when n=3,4.

NOTE:  The seminar has a webpage where the semester's program is listed:

http://www2.math.binghamton.edu/p/seminars/topsem
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