Local geometry of real and complex analytic mappings

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My work is at the interface of analytic geometry and commutative algebra, two major branches of modern mathematics with applications in science and engineering. They deal with the analysis of polynomial and analytic functions and the geometry of the spaces on which they live. The subject of my current research program is the study of the local degeneracies in mappings. Such minute degeneracies can completely destroy the geometric regularity of the objects defined by the mappings, and hence it is important to know how to detect them. The main task of my program is to establish simple algebraic criteria to control the local behaviour of a mapping. This research provides opportunities for the training of graduate students and postdoctoral fellows and involves international collaboration with other mathematicians.