Department of Mathematics

Indian Institute of Science

Bangalore 560 012






Dr.  Shane DīMello 
Affiliation : IISER, Pune

Subject Area






Department of Mathematics, Lecture Hall I




04:00 PM




October 25, 2016 (Tuesday)



"Some results on the topology of real algebraic curves"


The topology of real algebraic varieties is the study of the topology of objects that can be defined real algebraically and particularly the restrictions that the real algebraic structure imposes on the topology. Hilbert's famous address motivated an interest in the so called Hilbert's sixteenth problem of classifying, up to isotopy, real algebraic curves of a given degree. While successful only up to degree 7, it has motivated many natural and interesting questions and generalizations. We will look at some of these questions including a criterion for curves that have the maximum permissible number of components in terms of the Jacobian of the complexification of the curve, the reduction of the classification of real planar rational quartics to the simple combinatorial classification of "extended" chord diagrams, the classification of real rational knots of low degrees, and an application of braid groups in constructing real rational representatives of knots.