Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by P lya in the 1930's and rediscovered in part several times since, it was not un

Sturm Theorems for Linear Parabolic Equations and Intersection Comparison. Transversality, Concavity and Sign-Invariants. B-Concavity and Transversality on Nonlinear Subsets for Quasilinear Heat Equations. Eventual B-convexity: a Criterion of Complete Blow-up and Extinction for Quasilinear Heat Equations. Blow-up Interfaces for Quasilinear Heat Equations. Complete and Incomplete Blow-up in Several Space Dimensions. Geometric Theory of Nonlinear Singular Parabolic Equations. Intersection Techniques in Generalized Free-Boundary Problems. Intersection Techniques for Solutions Changing Sign. Discontinuous Limit Semigroups for the Singular Zhang Equation and Generalizations. Further Examples of Discontinuous and Continuous Limit Semigroups.