Gun violence is a central public concern in the United States, annually leading to the deaths of 36,000 individuals and the non-fatal injuries of 85,000 others. It has been called an epidemic and a public health crisis. In May of 2019, a diverse group of researchers participated in a workshop at the University of Tennessee, Knoxville. This workshop was sponsored by the Center for the Dynamics of Social Complexity (DySoC) and the National Institute for Mathematical and Biological Synthesis (NIMBioS). The objectives of this workshop were to review the existing approaches on the mathematics and modeling of gun violence, identify and prioritize areas in the field that require further research, develop cross-disciplinary collaborations to gain new perspectives, and suggest research and data collection that could assist evidence-based policy recommendations. The purpose of this report is to present some of the responses to the mentioned objectives and to suggest areas of future research .