The computation of the higher genus Gromov-Witten invariants of compact Calabi-Yau 3-fold has been a central and yet difficult problems in geometry and physics. During last a few years, a dramatic progress has been achieved.

Founded in 1796, University of Strathclyde (Glasgow) has now become one of the leading technological universities globally.

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.