1088 NOTICES OF THE AMS VOLUME 65, NUMBER 9 The purpose of a Geometry Lab is to foster a community to promote research involving all stages of academia, provide mentoring experiences to early career mathematicians, and disseminate mathematics beyond the boundaries of the university. Breakthroughs in science and mathematics often come from experimentation, computation, and communication of technical facts to non-experts. Geometry Labs (also known as Experimental Mathematics Labs) espouse this approach with vertically integrated groups of students and researchers advancing mathematics through experimentation, visualization, and public engagement. The research community at the core of an experimental mathematics lab produces a synergistic experience: the undergraduates’ research resonates with their coursework; graduate students’ research blends with mentoring; and faculty foster a deeper connection between research and teaching. In parallel, this shared experience informs public engagement activities that bridge the gap between science and society, paving the way for the next generation of researchers. Geometry Labs United: An Invitation