Holm is an expert in symplectic geometry and its interactions with algebraic geometry, topology and combinatorics. Her research has been supported by the National Science Foundation, the Association for Women in Mathematics, and the Simons Foundation. In 2012, Holm was named a Fellow of the AMS. In 2014, Holm was an Oliver Smithies Lecturer and Visiting Fellow at Balliol College, Oxford, and a von Neumann Fellow at the Institute for Advanced Study, Princeton. Holm was a Project NExT Fellow in 2005-06, is a member of the Board of Directors of the Budapest Semesters in Mathematics, and is a member of the leadership team of Transforming Post-Secondary Education in Mathematics.