Multiplicative kernels, Non-abelian Abel theorem, Kontsevich polynomials and around. Part 1

We discuss recent progress (published and unpublished yet ) in studies of multiplicative kernels, initiated by M. Konstevich. We will try to explain various links and applications of this notion in geometry, differential equations and integrable systems. My talk is based on the paper arXiv:2102.09511 and on two ongoing projects with I. Gaiur and D. Van Straten.