BOWLING GREEN STATE UNIVERSITY
          DEPARTMENT OF MATHEMATICS AND STATISTICS CALENDAR
 
                   Week of September 29 - October 3

Monday, September 29

 3:30 INVITED STATISTICS SEMINAR  - Room 459 MSC
      Lev Klebanov, BGSU and St. Petersburg State University
                             for Architecture and Civil Engineering
      Model Construction in Statistical Estimation Theory

Tuesday, September 30

11:30 ALGEBRA SEMINAR  - Room 447 MSC
      Steve McCleary, Dept. of Mathematics and Statistics, BGSU
      "Antique totally ordered sets"     

 2:30 ANALYSIS SEMINAR  - Room 459 MSC
      Alex Izzo, Dept. of Mathematics and Statistics, BGSU
      "Gelfand theory"

Thursday, October 2

 3:30 SCIENTIFIC COMPUTING SEMINAR  - Room 459 MSC
      Gordon Wade, Dept. of Mathematics and Statistics, BGSU
      "Some elementary quadrature and approximation properties 
       of orthogonal polynomials"

Friday, October 3

 3:30 Coffee
 3:45 COLLOQUIUM  - Room 459 MSC
      Tim Hsu, University of Michigan
      "Coxeter's kaleidoscope; or, What is geometric group theory?"
      Abstract: A Coxeter group (for the purposes of this talk) is a
        discrete group generated by reflections in Euclidean n-space.
        For example, the group generated by the reflections in the
        sides of a square in the Euclidean plane is a Coxeter group,
        as are the groups generated by the reflections in the sides of
        an equilateral triangle or an isoceles right triangle.

        Following Coxeter's own proof (Chapter 5 of his book Regular
        Polytopes, or his paper of 1934), we show that every Coxeter
        group has a presentation, or abstract definition, of the form

           <R_i | 1 = R_i^2 = (R_i R_j)^{m_{ij}}>,

        where the R_i correspond to the reflections in a certain
        well-chosen set of generating mirrors, and \pi/m_{ij} is the
        dihedral angle between mirror i and mirror j (necessarily an
        integer).  The main principles of this proof turn out to be
        fundamental ideas in the subject known as geometric group
        theory, and so we will also discuss what geometric group
        theory is, with some examples of recent Coxeter-like ideas and
        results.  In particular, if time permits, we will mention some
        of the author's recent work (joint with Dani Wise) on
        non-positively curved polygons of finite groups, a natural
        generalization of infinite planar Coxeter groups.

        The only background needed for this talk is a first course in
        group theory (for instance, as part of a larger course on
        abstract algebra).  Some familiarity with presentations will
        be helpful, but not necessary.


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