Riemann Hypothesis for Plane Curve Singularities
Explore the intricacies of local factors in the Hasse-Weil zeta-function and L-functions of curve singularities over finite fields in this comprehensive lecture. Delve into the concept of motivic superpolynomials and their conjectured relationship with Galkin-Stohr L-functions for plane curve singularities. Examine the definition based on quot-type schemes of torsion-free modules and their connection to affine Springer fibers. Investigate the conjectured equivalence between motivic superpolynomials, DAHA-superpolynomials, and reduced Khovanov-Rozansky polynomials of algebraic links. Learn about the Riemann Hypothesis for motivic superpolynomials and its conditions. Discover potential applications in number theory, low-dimensional geometry, and physics, referencing the work presented in https://arxiv.org/abs/2304.02200.