In this talk we will try to explain what is Equivariant Topological Combinatorics by discussing several problems of convex geometry, like Tverberg type coincidence problems, Grünbaum–Hadwiger–Ramos hyperplane mass partition problem and equal area – equal perimeter polygon cutting problem from Nandakumar & Ramana-Rao.

Using the configuration space/test map ansatz we construct a bridge that connects the convex geometry problems with particular problems from (equivariant) topology. Advanced machinery of (equivariant) algebraic theory is used efficiently in addressing these problems.