MCS Seminar, Nov 16

Posted on November 11th, 2004 by

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)

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.

Dan Singer is an Assistant Professor in the Department of Mathematics
and Statistics at Minnesota State University, Mankato.

For the MCS seminar schedule see

If you or someone you know is interested in giving a talk this year,
contact David Wolfe at or San Skulrattanakulchai at


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