Chessboard complexes indomitable

We give a simpler, degree-theoretic proof of the striking new Tverberg type theorem of Blagojević, Ziegler and Matschke. Our method also yields some new examples of “constrained Tverberg theorems” including a simple colored Radonʼs theorem for d+3 points in Rd. This gives us an opportunity to review some of the highlights of this beautiful theory and reexamine the role of chessboard complexes in these and related problems of topological combinatorics.