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Equilevel algebras
V. A. Vassiliev
Singular knots are smooth maps that have self-intersections or points at which the derivative vanishes. We describe an algebraic classification of their sin…
Complements of caustics of real function singularities
V. A. Vassiliev
We study the topology of complements of caustics of function singularities of low codimensions, in particular 1) complete the enumeration of connected components of the complements…
Integrable bodies in odd-dimensional spaces
V. A. Vassiliev
V. Arnold's problem 1987-14 asks whether there exist smooth hypersurfaces in (other than the conics in odd-dimensional spaces) for which the volume of the segment cut by any…
Lacunas and local algebraicity of volume functions
Victor A. Vassiliev
The volume cut off by a hyperplane from a bounded body with smooth boundary in never is an algebraic function on the space of hyperplanes: for k=1 it is the famous lemma X…
A few problems on monodromy and discriminants
V. A. Vassiliev
A problem list in singularity theory. Most of these problems are related with the algorithmic enumeration of possible topological types of non-discriminant Morsifications of real f…