Postdoc

The  Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences announces a postdoctoral position in the field of Coding Theory, funded by the Bulgarian Research Program PIKOM (ПИКОМ). Duration of the position is 6 or 12 months, extendable for up to 36 months. Successful candidates will work in the department "Analysis, Geometry and Topology" and be affiliated with the International Center for Mathematical Sciences, Sofia (ICMS-Sofia), which is part of the Institute of Mathematics and Informatics.

Field: Geometry and topology of singularities

Supervisor: Dr. Antoni Rangachev

Brief annotation: A major theme in algebraic geometry is to understand how 

algebraic varieties or morphisms change in families. In singularity theory one is interested in the change of  the geometry and topology of complex singularities as they vary continuously in a family. For a given family family, the changes, as one moves from a particular fiber to a nearby fiber, can be observed on the level of  total space. The goal is to detect the changes by taking probes from the individual members of the family. These probes usually come in the form of numerical invariants. When there are no changes in the fibers in a certain sense,  we say that the family is equisingular. One ongoing project that is of interest to us is to find numerical control using multiplicity-type invariants for various forms of equisingularity including Zariski and Lipschitz equisingularity. Another project is to understand the generic deformations of singularities using algebraic invariants, conormal spaces and polar varieties, paying special interest to the class of singularities that do not admit smoothings.