Quadratic Forms in Surface Automorphisms and Singularity Theory

Explore a 50-minute conference talk on the study of nilpotent parts of pseudo-periodic automorphisms on real oriented surfaces with boundary. Delve into the association of a quadratic form with the first homology group and its applications in singularity theory. Learn about the twist formula and mapping class group theory techniques used to prove the positive definiteness of the form under specific conditions. Examine the case of monodromy automorphisms of Milnor fibers for germs of curves on normal surface singularities. Cover topics including periodic surfaces, classification, correlation numbers, intercession, and semistable reduction in surface singularity theory.