Tuesday, July 2nd, 2013
2:30pm - 3:30pm, in Science 2-064

Marina Ville

Université François Rabelais, Tours, France

An introduction to singularity theory of curves: the example of the cusp

Abstract: Algebraic geometry takes a polynomial and studies the set of points where it vanishes. Singularity theory focuses on the parts of this set which are not smooth, i.e. do not locally resemble a disk or a ball; it is an exciting field, where geometry, topology, algebra and hands on computations interact. I will give a flavor of singularity theory of complex curves by looking at the equation z_1^3-z_2^2=0 in the neighborhood of (0,0): the corresponding curve (the zero-set of the equation) is a non smooth cusp. After recalling the basics about knots, I will describe how a singular point in an algebraic curve defines a knot and I will show a picture of the trefoil knot which we get in our example.