Anna Huber Randomized Rounding on Hypergraphs A randomized rounding of a vector is a rounding that is generated at random in such a way that each component is rounded up with probability equal to its fractional part, not necessarily independently. The theorem of Beck and Fiala (1981) asserts that for every hypergraph and every vector of vertex weights there is a rounding of the weights such that the additive rounding error for each hyperedge is bounded by the hypergraph's maximum degree. I will talk about generalizations of this theorem to randomized roundings. The main idea is to use dependencies so as to obtain results that are superior to those obtained via independent randomness. Joint work with Benjamin Doerr, Jan Foniok and Christian Klein.