Explore the intricacies of pseudoholomorphic curves with boundary in this Members' Seminar talk by Sara Tukachinsky from the Institute for Advanced Study. Delve into Gromov-Witten theory, examining the moduli space of sphere maps and the challenges of open Gromov-Witten theory. Discover the speaker's approach to the invariance problem, developed jointly with Jake Solomon, including the strong Maurer-Cartan equation and the mapping cone complex. Gain insights into the relative quantum product and its associativity as Tukachinsky addresses the fundamental question: Can we truly count pseudoholomorphic curves with boundary?