Skip to main content

Singularity Theory

Singularity theory is at the crossroad of several mathematical disciplines, such as algebraic and analytic geometry, algebraic and geometric topology and differential geometry. Lately even connections with number theory have been found. It studied phnomena which undergo qualitative changes or bifurcations under small perturbation of the parameters of the problem in question. It finds aplycations in physcal sciences, robotics, criptography...

Singularity Theory research at ICMAT deals mainly with the algebro-geometric and topologycal aspects. It involves the study of algebraic and analytic singularities from different perspectives. Specific topics are the vanishing cohomology of singularities with its D-module and Hodge structure, the topology of the Milnor fibrarion, the embedded topology of the link, equisingularity, resolution in characterisric zero and p (including algorithmic aspects), hypersesolutions and descent categories, versal deformations and their base spaces with additional structure, invariants of surface singularities and of complex analytic spaces (including relations with gauge theoretic invariants), rational cuspidal curves, arrangements, arcs spaces and motivic integration, and relations with contact and symplectic geometry.