Week of November 15 - 19

Monday, November 15

 7:30 KME PRESENTATION  - Room 459 MSC

      Have you ever wondered what you can do with your math interest
      and knowledge outside regular classes at BGSU?  There are great
      opportunities available for undergraduates with math interest!
      This Monday, November 15, KME will be hosting a presentation on
      some of these opportunities.  We will provide information on
      summer positions and study abroad opportunities in mathematics.
      BGSU students who have participated in some of the programs will
      be there to speak and answer questions.  The atmosphere of the
      presentation will be very relaxed; students will be encouraged
      to ask questions and get involved in discussion.  If you are at
      all interested in expanding your math horizons, I highly suggest
      you come!

      The presentation will be at 7:30PM in room 459 of the Math
      Science building.  We will provide refreshments, and ALL
      STUDENTS ARE WELCOME TO ATTEND, regardless of their math
      background.  Please join us and learn what the world has to
      offer!

Tuesday, November 16

 2:30 ALGEBRA SEMINAR  - Room 447 MSC
      Ramiro Lafuente-Rodriguez, Mathematics and Statistics, BGSU 
      "Groups of divisibility"
      Abstract: We will look at the connection between abelian
        l-groups and the theory of integral domains using groups of
        divisibility.  If D is an integral domain with group of units
        U and field of quotients K, the group of divisibility of D is
        K*/U. For this purpose we'll study Bezout domains (domains in
        which every finitely generated ideal is principal).

 2:30 SCIENTIFIC COMPUTATION SEMINAR  - Room 459 MSC
      Ryan Mears, Department of Psychology, BGSU
      "Analysis of electrophysiological signals using wavelets and
       estimating instantaneous spectral information"

Wednesday, November 17

 2:30 ANALYSIS SEMINAR  - Room 459 MSC
      Juan Bes, Mathematics and Statistics, BGSU
      "Hypercyclic manifolds, IV"
      Abstract: We describe work of F. Leon and A. Montes on spectral
        conditions for an operator T acting on an (infinite dimensional)
        Hilbert space to have a closed, infinite dimensional linear
        subspace where every non-zero vector is hypercyclic for T.

Friday, November 19

 3:30 Refreshments
 3:45 COLLOQUIUM  - Room 459 MSC
      David Grabiner, Mathematics and Statistics, BGSU 
      "Brownian motion in a Weyl chamber, non-colliding particles, and
       random matrices"
      Abstract: Let n particles move in standard Brownian motion in one
        dimension, with the process terminating if two particles collide.
        This is a specific case of Brownian motion constrained to stay
        inside a Weyl chamber; the Weyl group for this chamber is
        A_{n-1}, the symmetric group.  For any starting positions, we
        compute a determinant formula for the density function for the
        particles to be at specified positions at time t without having
        collided by time t.  We show that the probability that there will
        be no collision up to time t is asymptotic to a constant multiple
        of t^{-n(n-1)/4} as t goes to infinity, and compute the
        constant as a polynomial in the starting positions.  We have
        analogous results for the other classical Weyl groups; for example,
        the hyperoctahedral group B_n gives a model of n independent
        particles with a wall at x=0.

        We can define Brownian motion on a Lie algebra, viewing it as a
        vector space; the eigenvalues of a point in the Lie algebra
        correspond to a point in the Weyl chamber, giving a Brownian motion
        conditioned never to exit the chamber.  If there are m roots in n
        dimensions, this shows that the radial part of the conditioned
        process is the same as the n+2m-dimensional Bessel process, which
        is the radial part of an n+2m-dimensional Brownian motion.  The
        conditioned process also gives physical models, generalizing
        Dyson's model for A_{n-1} corresponding to u_n of n particles
        moving in a diffusion with a repelling force between two particles
        proportional to the inverse of the distance between them.