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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, January 9, 2001}
\centerline{Sequoia Hall Rm. 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Steven N. Evans}
\centerline{\sl Statistics and Mathematics}
\centerline{\sl U.C. Berkeley}
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\centerline{\bf DNA, Family Trees, Elimination Ideals, Groups, and Z-Modules}
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The method of invariants is an approach to the problem of reconstructing
the evolutionary family tree for a number of species using DNA sequence
data.  In order to apply this method, one needs to solve a problem in
commutative algebra: how to find all the algebraic relationships between a
certain collection of polynomials in a large number of variables. We show
how some simple finite group Fourier analysis reduces this problem to one
of linear algebra that can be solved by efficient algorithms.  We also
indicate how these ideas can be used to show that the method of invariants
can always distinguish between different family trees.  This is joint work
with Terry Speed and Xiaowen Zhou.



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