Section: Highlights of the Year

Highlights of the Year

In the context of drawing plane algebraic curves with the correct topology, we have obtained and submitted this year major results on the resolution of bivariate algebraic systems. In particular, we presented algorithms whose worst-case and expected (Las Vegas) complexities are not likely to be easily improved as such improvments would essentially require to improve bounds on other fundamental problems (such as computing resultants, checking the squarefreeness of univariate polynomials, and isolating their roots) that have hold for decades. See section  7.3.1 for details.