One of most difficult problems in geometry and physics is to compute higher genus Gromov-Witten (GW) invariants of compact Calabi-Yau 3-folds such as quintic 3-folds.

A cyclic extension of the classical notion of descents for permutations was introduced by Klyachko and Cellini, leading to a rich variety of applications and implications.

The set values have been introduced for many applications, such as time inconsistent stochastic optimization problems, multivariate dynamic risk measures, and nonzero sum games with multiple equilibria.