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By Ernst Dieterich and Lars Lindberg

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1979-10. Describe the mixed Hodge structures of superpositions of functions. 1979-11. Investigate typical singularities of the boundary of the time-like attainability domain. 1979-12. Investigate the singularities of the time of shortest bypass of an obstacle. 1979-13. Is it true that the singularities of the boundary of the attainability domain in a generic controlled system are the same as those of a generic projection of a manifold with boundary? More generally, a "parameter" in optimization problems is a choice of control from a function space (which can have a boundary or other singularities).

However, for T 2 and S2 this conjecture has not been disproved. 1981-10. Construct a bifurcation theory for optical caustics, in particular, prove that "flying saucers" caustics do not exist. 1981-11. Find a Lagrangian singularity related to the hypericosahedron group H4. 1981-12. Find the (Zariski) relations between the (Zariski) relations of swallowtails (and, in general, explore "syzygies," or "noncommutative resolvents" of the 1981-12 The Problems 45 fundamental groups of complements of algebraic hypersurfaces, associated with the sequence of complete flags of generic projections, and with generators and relations of the sequence of the fundamental groups of complements of discriminants of those projections).

1975-12. Does every real-valued function have a real Modification (with \i real critical points)? 1975-13. What is the minimal number of critical values obtained by a perturbation of a critical point of multiplicity \i with (i Morse critical points? Conjecturally it is n + 1, where n is the number of variables (or corank). 1975-14. Is the corank a topological invariant? 1975-15. What singularities can absorb Ai? split Ai off? Why is every stratum |x = const connected to the stratum A\ by a chain of strata of all codimensions?

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