Geometry: Adam Parusinski -- Geometry

Newton polygon relative to an arc

We give an elementary introduction to the singularity theory
of complex polynomials of two variables.
Let P(x,y) be such a polynomial, P(0,0)=0.  Newton showed how to
find the solutions y(x) of the equation P(x,y(x)) = 0, using the (Newton)
polygon method.  We generalize  this construction to study
the polar curves, Lojasiewicz exponents, singularities at infinity, and
equi-singular deformations.
(707A, August, Wednesday 12, 19, 11-12, and Wednesday 26, 11-13)

These lectures are mainly designed for students.