# Topology and Combinatorics of 'unavoidable' complexes and the family tree of the Van Kampen-Flores theorem

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Special classes of simplicial complexes (chessboard, unavoidable’, threshold, simple games’, etc.) play a central role in applications of algebraic topology in discrete geometry and combinatorics. As an illustration we outline the proof of a (so far) the most general theorem of Van Kampren-Flores type  (arXiv:1502.05290 [math.CO], Theorem 1.2), confirming a conjecture of Blagojevic, Frick, and Ziegler (Tverberg plus constraints, Bull. London Math. Soc., 46 (2014) 953-967).  The results presented in the lecture are a joint work with Dusko Jojic (University of Banja Luka) and Sinisa Vrecica (University of Belgrade).