The "colored Tverberg problem" asks for a smallest size of the color classes in a (d+1)-colored point set C that forces the existence of an intersecting family of r "rainbow"
simplices with disjoint, multicolored vertex sets from C.
Using relative equivariant obstruction theory applied to a modified problem, we prove the optimal lower bound conjectured by Barany and Larman (1992) for the case of partition into r parts, if r+1 is a prime.
(Joint work with Pavle V. Blagojevic)
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