Department of Mathematics

Indian Institute Of Technology Madras , Chennai

Newton Polygons and solving equations.

Speaker : Sarang Sane, Department of Mathematics, IIT Madras.

19-02-2019

Abstract :

Consider a polynomial equation f(X,Y) in two variables (e.g. Y^6-5XY^5+X^3 Y^4-7X^2 Y^2+6X^3+X^4 = 0) . How do we solve for Y in terms of X, thus obtaining solutions to such an equation? In the talk, we will describe Newton polygons, work through example(s) (e.g. the one mentioned above whose solution Newton described) and outline Newton's method (a precursor to the Newton-Raphson method) of how to obtain these solutions as a Puiseux series. Time permitting, we will attempt at giving a rigorous explanation of why it works. For most part, the talk needs no specialised knowledge and should be widely accessible.

Key Speaker Sarang Sane, Department of Mathematics, IIT Madras.
Place NAC 505
Start Time 3:00 PM
Finish Time 4:00 PM
External Link None