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Towards a Combinatorial Proof of the Quadratic Case of
the Jacobian Conjecture
Dan Singer
CANCELLED (was: Tuesday, November 16, 2003 at 3:30pm in Olin 320)
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The Jacobian Conjecture states that a system F=(F_1,…, F_n)
of n polynomials in n variables over a field with characteristic zero
has a polynomial inverse if and only if
$hbox{det}({partial F_iover partial x_j})$
is a non-zero scalar in that field. The quadratic case has been shown
to be true, as have a variety of other special cases, but the
full conjecture remains open. In this talk we will describe how an
understanding of the algebraic combinatorics associated with a
ring and module generated by rooted planar binary trees may yield
a combinatorial proof of the quadratic case. The modest results we
have obtained so far suggest that there are Ramsey-theory type
theorems about trees waiting to be discovered.
Refreshments will be served.
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Dan Singer is an Assistant Professor in the Department of Mathematics
and Statistics at Minnesota State University, Mankato.
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For the MCS seminar schedule see
http://www.gac.edu/oncampus/academics/mcs/mcs-seminar/
If you or someone you know is interested in giving a talk this year,
contact David Wolfe at wolfe@gustavus.edu or San Skulrattanakulchai at
sskulrat@gustavus.edu.