School of Mathematics Colloquium

Curvettes and Jacobian Problem

by Prof. S.S. Abhyankar (Purdue University, USA)

Thursday, December 15, 2011 from to (Asia/Kolkata)
at Colaba Campus ( AG-69 )
Description
Dicritical Divisors are a new tool of attacking the famous
Jacobian Problem. Curvettes are a new way of looking at Dicritical Divisors.
A Curvette is a snake-like quadratic sequence risiing from the base ring to
a prime divisors. They induce an approximate factorization of a two variable
polynomial which may or may not have a jacobian mate.

Dicritical Divisors reminded me of Spiders in the Marathi Poem
`EKA KOLIYANE EKADA APULE JALE BANDHIYELE....'
A Curvette reminds me of the Nag-Panchami Baj Exihibition in a MANDIR in
Gwalior
where I grew up, and a curvette-pair is like the NAGAPASHA released by
Indrajit.
Just as spiders were joint work with Ignacio Luengo,
snakes are joint work with Enrique Artal.