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Below are the most common reasons: This site uses cookies to improve performance by remembering that you are logged in when you go from page to page.To provide access without cookies would require the site to create a new session for every page you visit, which slows the system down to an unacceptable level.The development of these results led to the construction of a complex of singularities and to the discovery of numerous restrictions on the coexistence of singularities.

In the last years Vassiliev has led an almost desperate but valiant struggle for mathematical education in Russia and worldwide.Vassiliev constructed, under very general assumptions, a spectral sequence computing the corresponding homology and yielding powerful invariants.He developed the stability theory for the cohomology of complements to discriminants.He invented explicit and efficient ways to compute topological characteristics of complements to discriminants, as well as implicit means to establish isomorphisms between these characteristics of different spaces.His spectral sequence, when applied to spaces of polynomials, stabilizes, which allows one to prove results of Smale–Hirsch type for spaces of maps with prescribed singularities.