New open r-spin theories

In his 92' work, Witten has defined the r-spin intersection theory. This theory have found an open counterpart, in genus 0,
in a recent joint work with Buryak and Clader. In the closed and open setting there are (internal) marked points, which are allowed to carry any twist from the set 0,1,...,r-1, and in the open setting there are also boundary markings whose twist is restricted to be r-2. My talk will describe a new construction of genus=0 open r-spin theories, which allows different collections of boundary states, as well as the relations satisfied by the resulting intersection numbers. If time permits I will also say a few words on higher genus. Based on a joint work with Yizhen Zhao.