| Résume | The Witten r-spin class is an example of a cohomological field theory which is not semi-simple, but it can be "shifted" to make it semi simple. Pandharipande-Pixton-Zvonkine studied the shifted Witten class and computed it explicitly in terms of tautological classes using the Givental-Teleman classification theorem. I will show that the R-matrix of (two specific) shifts can be obtained from two differential equations that are generalizations of the classical Airy differential equation. Using this, I will show that the descendant intersection theory of the shifted Witten classes can be computed using the Eynard-Orantin topological recursion, and discuss some potential applications. This is based on work in progress with S. Charbonnier, A. Giacchetto and E. Garcia-Failde. |
