The satellite workshop on “singularities in real and complex geometry” will take place on Friday June 16, 2017, 14h17h.

 Michel Coste, Rationality of the set of singular poses of a GoughStewart platform
The GoughStewart platform is a rather wellknown parallel robot with 6 degrees of freedom. The singular poses are those for which the platform loses mobility. We show that, for a general GoughStewart platform, the set of these singular poses is a rational variety in the group of rigid motions. The proof relies on the classical theory of cubic surfaces.  Krzysztof Kurdyka, Convexifying positive polynomials and a proximity algorithm
We prove that if f is a positive C^{2 }function on a convex compact set X then it becomes strongly convex when multiplied by (1+x^{2})^{N} with N large enough. For f polynomial we give an explicit estimate for N, which depends on the size of the coefficients of f and on the lower bound of f on X. As an application of our convexification method we propose an algorithm which for a given polynomial f on a convex compact semialgebraic set X produces a sequence (starting from an arbitrary point in X) which converges to a (lower) critical point of f on X. The convergence is based on the method of talweg which is a generalization of the Lojasiewicz gradient inequality. (Joint work with S. Spodzieja, published in SIAM Opt. 2016).
 Mihai Tibar, The bifurcation locus of polynomial maps
Presentation of some recent results concerning the problem of detecting the locus where a polynomial map F: K^n \to K^p is not a locally trivial fibration (K= R or C), with view to effectivity aspects.
 Zbigniew Jelonek, On semiequivalence of polynomial mappings
Let f: X>Y be continuous mappings. We say that f is topologically equivalent to g if there exist homeomorphisms P:X>X and Q: Y>Y such that f=Q g P. Moreover, we say that f is topologically semiequivalent to g if there exist open, dense subsets U,V c X and homeomorphisms P:U>V and Q: Y>Y such that g=Q f P. Let X, Y be smooth irreducible affine complex varieties. We show that every algebraic family F: M x X>Y of polynomial mappings contains only a finite number of topologically nonequivalent proper mappings and only a finite number
of topologically nonsemiequivalent genericallyfinite mappings. In particular there are only a finite number of classes of topologically nonequivalent proper polynomial mappings f: C^{n}>C^{m} of a bounded (algebraic) degree. The same is true for a number of classes of topologically nonsemiequivalent genericallyfinite polynomial mappings f:C^{n}>C^{m} of a bounded (algebraic) degree.  On conjectures of Chudnovsky and Demailly and Waldschmidt constants
For a subvariety Z in projective space one defines its initial sequence alpha_m(Z) as the least degree of nonzero elements in symbolic powers of the saturated ideal I=I(Z). The asymptotic invariant attached then naturally to Z is its Waldschmidt constant defined as {alpha^}(I)=inf {alpha_m(Z)}/{m}.
These invariants have been studied in complex analysis some 40 years ago and resurfaces recently in problems related to the containment relations between ordinary and symbolic powers of homogeneous ideals.
I will report on these new developments and challenging conjectures which remain open for quite long.
The workshop is supported by UCAJedi.
 Michel Coste, Rationality of the set of singular poses of a GoughStewart platform