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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.