From Thom's Gradient Cell Decomposition to the Curvature of Milnor Fibers

Explore the evolution of mathematical concepts in this 56-minute lecture by Bernard Teissier from the Institut des Hautes Etudes Scientifiques (IHES). Delve into the early 1970's work of Thom on gradient cell decomposition for the Milnor fiber of isolated complex hypersurface singularities. Discover how Thom's attempt to prove the finiteness of monodromy led to the recognition of the geometric significance of polar curves associated with singularities and general hyperplane directions. Examine the various applications of polar curves in obtaining algebraic, topological, and Lipschitz-geometric information about isolated hypersurface singularities. Gain insights into the progression from Thom's initial ideas to the current understanding of Milnor fiber curvature.