18 citations · 51 across the 30 of their papers we have counts for
35 papers
Inscribed squares of level sets of functions on the sphere
V. A. Vassiliev
According to a theorem by F.~Dyson, every continuous function takes the same value at the vertices of a square inscribed into a great circle of . We g…
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…
Average intersection number of trigonometric plane curves in and statistics
V. A. Vassiliev
The average value of the number of intersection points of two plane curves given by trigonometrical polynomial maps of degree and bounded - or - norms is calculated
Algebraically integrable bodies and related properties of the Radon transform
Mark Agranovsky, Jan Boman, Alexander Koldobsky +2
Generalizing Lemma 28 from Newton's ``Principia", Arnold asked for a complete characterization of algebraically integrable domains. In this paper we describe the current state of A…
Complements of discriminants of real parabolic function singularities
V. A. Vassiliev
A (conjecturally complete) list of components of complements of discriminant varieties of parabolic singularities of smooth real functions is given. We also promote a combinatorial…
Cohomology of spaces of complex knots
V. A. Vassiliev
We develop a technique for calculating the cohomology groups of spaces of complex parametric knots in , , and carry out these calculations to obtain these…
Varieties of chord diagrams, braid group cohomology and degeneration of equality conditions
Victor A. Vassiliev
For any finite-dimensional vector space of continuous functions consider subspaces in defined by systems of {\em e…
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…
New Examples of Irreducible Local Diffusion of Hyperbolic PDE's
Victor A. Vassiliev
Local diffusion of strictly hyperbolic higher-order PDE's with constant coefficients at all simple singularities of corresponding wavefronts can be explained and recognized by only…
New examples of locally algebraically integrable bodies
Victor A. Vassiliev
Any compact body in with smooth boundary defines a two-valued function on the space of affine hyperplanes: the volumes of two parts into which these hyperplanes cut…
Twisted homology of configuration spaces, homology of spaces of equivariant maps, and stable homology of spaces of non-resultant systems of real homogeneous polynomials
Victor Vassiliev
A spectral sequence calculating the homology groups of some spaces of maps equivariant under compact group actions is described. For the main example, we calculate the rational hom…
Homology of the complex of not 2-divisible partitions
Victor A. Vassiliev
The rational homology group of the order complex of non-even partitions of a finite set is calculated. A twisted version of the Goresky-MacPherson approach to similar homology calc…
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…
Rational homology of configuration spaces of the Moebius strip and projective plane
Victor A. Vassiliev
All rational homology groups of unordered configuration spaces of the Moebius strip and the projective plane are calculated
Multiplicities of bifurcation sets of Pham singularities
Victor A. Vassiliev
The local multiplicities of the Maxwell sets in the spaces of versal deformations of Pham holomorphic function singularities are calculated. A similar calculation for some other bi…
Linking numbers in non-orientable 3-manifolds
Victor A. Vassiliev
The construction of integer linking numbers of closed curves in a three-dimensional manifold usually appeals to the orientation of this manifold. We discuss how to avoid it constru…
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…
Rational homology of the order complex of zero sets of homogeneous quadratic polynomial systems in
Victor A. Vassiliev
The naturally topologized order complex of proper algebraic subsets in , defined by systems of quadratic forms, has rational homology of
Homology groups of spaces of non-resultant quadratic polynomial systems in R^3
Victor A. Vassiliev
We calculate rational homology groups of spaces of non-resultant (i.e. having no non-trivial common zeros) systems of homogemeous quadratic polynomials in R^3
Homology of spaces of non-resultant polynomial systems in R^2 and C^2
V. A. Vassiliev
The resultant veriety in the space of systems of homogeneous polynomials of given degrees consists of such systems having non-trivial solutions. We calculate the integer cohomology…
Complexes of connected graphs
V. A. Vassiliev
Graphs with given k vertices generate an (acyclic) simplicial complex. We describe the homology of its quotient complex, formed by all connected graphs, and demonstrate its applica…
Monodromy of complete intersections and surface potentials
Victor A. Vassiliev
Following Newton, Ivory and Arnold, we study the Newtonian potentials of algebraic hypersurfaces in . The ramification of (analytic continuations of) these potential depends o…
On -neighborly submanifolds in
Victor A. Vassiliev
A submanifold is -neighborly if for any points in there is a hyperplane, supporting and touching it at exactly these points. We prove that the mi…