Riemann Hypothesis for Zeta-functions of Plane Curve Singularities

Zeta-functions of plane curve singularities will be defined from scratch and discussed, including basic examples. The functional equation for them holds, however the Riemann Hypotheis fails for the corresponding L-functions in contrast to the smooth projective curves (Weil, Deligne). This can be fixed for sufficiently small q. Classically q is the cardinality of a finite field, but it becomes an arbitrary parameter in the new vintage of the theory, inspired by the connections with motivic and DAHA superpolynomials, and with Khovanov-Rozansky ones. The motivic superpolynomials will be fully defined; their relation to affine Springer fibers will be discussed at the end. Only very basic knowledge of rings/modules is assumed and no theory of curves and their singularities will be used.