Gregory Mikhalkin
(Geneva)
"Real algebraic knots and links"
Abstract:
Topology of algebraic curves of given degree in the real plane is a classical subject studied for over a hunder years after its inclusion by Hilbert to his famous list of problems. However the "visible" topology here is actually reduced to combinatorics because of restriction to dimension 2. In the same time the corresponding 3-dimensional problem belongs to the realm of knot theory. The talk will survey the corresponding 3-dimensional problem. In particular, it will contain topological classification of degree 5 curves of any genus in RP3 (a joint work with S. Orevkov). A special attention will be paid to tropical constructions of real curve that generalize Viro patchworking to higher dimensions.