Andrei Căldăraru
University of Wisconsin-Madison, Madison WI, USA

Catgeorical Enumerative Invariants were introduced by Costello (2005) and, in a different form, by Cotello, Tu, and the author (2020). They are a sequence of numerical invariants associated to a Calabi-Yau category and a splitting of its non-commutative Hodge filtration. In my talk I will survey recent progress in computing such invariants for elliptic curves (generalizing GW, FJRW and BCOV theories in enumerative geometry/mirror symmetry) and for rational surface singularities (generalizing Saito theory in singularity theory). This talk is based on joint work with Junwu Tu, Si Li, Yunfan He, Weng-Him Cheung.