Conference: Contemporary Trends in Hamiltonian Geometry

The conference, "Contemporary Trends in Hamiltonian Geometry" will take place September 27-October 2, 2026, at the SwissMap Research Center in Les Diablerets, Switzerland. Hamiltonian geometry originated as a powerful framework for revealing and exploiting symmetries to describe physical principles such as conservation of energy and momentum. Its success as a framework for physics persists from classical mechanics through quantum mechanics, impacting much of modern physics as well as important applications such as robotics. Hamiltonian geometry is currently a flourishing area of symplectic geometry that is necessarily cross-disciplinary, with many connections to other scientific fields. The proposed conference in Les Diablerets will bring together both experts and junior researchers, at a moment of rapid development and expansion in the field. A key goal of the conference is to form new research collaborations and determine the direction of research in the years to come. This funding will enable U.S. researchers to participate in the conference. The broader impact of the funding includes the training of U.S. early-stage researchers, the establishment of new connections between researchers across mathematical sub-disciplinary boundaries, and the dissemination of exciting results in Hamiltonian geometry to an international audience. More formally, this conference will examine key questions of outstanding significance in Hamiltonian geometry. These include the classification of complexity-one spaces, combinatorial and topological characterization of Hamiltonian circle actions, Schubert calculus and its generalizations, quantization and reduction with varying geometric structures, the tropical-to-Lagrangian correspondence, and the distinctions between algebraic versus symplectic classifications. The conference as a whole will foster collaboration and connections across related fields of mathematics, while helping to train young researchers and identify the most important questions emerging within the field. More information is available on the conference website: https://swissmaprs.ch/events/contemporary-trends-in-hamiltonian-geometry/ This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria. NSF Award ID: 2540714 | Program: 01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Rebecca Goldin | Institution: George Mason University, FAIRFAX, VA | Award Amount: $30,000 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2540714 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2540714.html