turkmath.org

I will address the following conjecture (and some refinements thereof): “A smooth plane curve of degree 6 has at most 72 tritangents.” After a brief introduction to the subject and a survey of the known results for the other polarized K3-surfaces, I will explain why the traditional approach does not work and suggest a new one, using the embedding of the Néron—Severi lattice of a K3-surface to an appropriate Niemeier lattice. I will also discuss the pros and contras of several versions of this approach and report the partial results obtained so far.