Colloquium abstracts

S.S. Abhyankar
Purdue University, USA
December 15, 2011

Curvettes and Jacobian Problem:  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.