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Wednesday, September 17, 2014

**Abstract:** In the first part of his sixteenth problem, Hilbert asks for an investigation of the ways in which the components of a real plane algebraic curve of degree d can be arranged. This problem was part of the impetus for the development of what is now known as **real** algebraic geometry. In this talk we will highlight a few of the differences between real and complex algebraic geometry (sticking to the context of curves). We will discuss the solution to Hilbert's question in degree 6, which was finished in 1969. Furthermore, we will indicate how isotopy classes can be studied via discriminants. Time permitting, we will try to give an idea of how toric geometry can be used to classify certain isotopy classes.