The Canadian Mathematical Society (CMS) is delighted to announce Emmy Murphy as the recipient of the 2025 Krieger-Nelson Prize. Murphy receives this prestigious award in recognition of her important and significant contributions to research, particularly in the fields of symplectic and contact geometry, as well as geometric topology.
Murphy earned her Ph.D. in Mathematics from Stanford in 2012. She then joined the Massachusetts Institute of Technology as a C. L. E. Moore Instructor, and eventually as an Assistant Professor. Afterward, she moved to Northwestern University, where she advanced from Assistant Professor to Associate Professor and later Full Professor. She subsequently became a Full Professor at Princeton before joining the University of Toronto in 2023, where she now holds a cross-appointed (UTM/UTSG) Full Professorship. Murphy has authored over 20 articles in prestigious research journals and has been an invited speaker at more than 125 colloquia, lectures, conferences, and seminars.
Murphy’s work is centered in the field of contact and symplectic topology and geometry. The field sheds light on the geometry of phase space and time-evolution in classical mechanics. Contact topology focuses on manifolds of odd dimensions, while symplectic topology deals with manifolds of even dimensions.
In her doctoral thesis, Murphy discovered a groundbreaking geometric flexibility phenomenon for Legendrian submanifolds in high-dimensional contact manifolds. Classifying Legendrian submanifolds up to isotopy is typically a complex problem, with intricate behaviors even in low dimensions, such as the subtle phenomena seen in Legendrian knots within the 3-sphere.
However, Murphy’s thesis revealed that for a special class of Legendrian submanifolds, called “loose” Legendrians, the classification simplifies dramatically. These submanifolds contain a specific local pattern that enables the entire contact topology to become flexible. As a result, their classification reduces to classical algebraic topology: two loose Legendrians are isotopic if and only if they share the same fundamental topological invariants, and any smooth submanifold satisfying the necessary basic topological conditions can be deformed into a loose Legendrian in a unique way.
This breakthrough resolved longstanding existence questions for Legendrian submanifolds and provided a complete classification for the loose case. In contrast, non-loose Legendrians exhibit rigidity, often detected using Floer-theoretic invariants, and remain much harder to classify.
Following her Ph.D., Murphy continued to explore flexibility phenomena in higher-dimensional contact and symplectic topology. In collaboration with her advisor Dr. Yasha Eliashberg, as well as Dr. Mathew Strom Borman, Dr. Roger Casals, and Dr. Francisco Presas, she clarified the fundamental nature of flexibility in higher-dimensional contact manifolds. Their work established that flexibility arises from the presence of a geometric structure called an “overtwisted disk” within the contact manifold (an insight that extends a classical result of Eliashberg’s in dimension 3).
This research provided definitive existence and uniqueness results for overtwisted contact structures, settling the question of which smooth manifolds can admit contact structures. It also offered a complete classification for the overtwisted case, in contrast to the more enigmatic tight contact structures, which remain a major area of study despite numerous classical and exotic examples. This work represents one of the most significant developments in contact topology since the early 2000s, alongside the revolutionary contributions of Chekanov, Eliashberg (on contact homology), and Giroux (on open book structures).
Murphy’s influential papers on looseness and overtwistedness have been published in Acta Mathematica and Geometry & Topology, two of the most selective journals in pure mathematics.
Beyond her foundational work on flexibility, Dr. Murphy has contributed to other important discoveries. In collaboration with Dr. Eliashberg, she established the existence and uniqueness of Lagrangian “caps”, which fill (from the outside) loose Legendrians. With her collaborator Dr. Kyler Siegel, she uncovered a surprising phenomenon: overtwisted (flexible) Stein domains can contain subdomains that are not flexible, even though most of their Floer-theoretic invariants vanish. These findings continue to shape the field, offering new perspectives on flexibility and rigidity in contact and symplectic topology.
Murphy’s nominators emphasized her exceptional impact on the field of contact topology and the high regard in which she is held by the international mathematical community. One noted:
“Murphy is arguably one of the most talented contact topologists of her generation worldwide, with an impressive track record of contributions at the highest level that have already reshaped the field.”
Another highlighted the significance of her appointment to the University of Toronto, stating:
“Her joining our department in 2023 has created a “wow” response among our international colleagues, and brings a boost to the Canadian mathematical community.”
Murphy’s contributions have been recognized by various prizes and awards, such as the Mathematical Congress of the Americas Prize (2021), the New Horizons in Mathematics Prize (2020), the AWM Birman Research Prize in Topology and Geometry (2017), the Académie Royale de Belgique prize for an original contribution to the existence of contact structures (2015), the UNR College of Science Distinguished Young Alumni of the Year (2015), and a Sloan Research Fellowship (2015), to name only a few.
In summary, Emmy Murphy’s important contributions to contact and symplectic topology have significantly advanced the field, earning her international recognition and numerous prestigious awards. Her innovative research on flexibility phenomena has reshaped the understanding of high-dimensional geometric structures, influencing both theoretical developments and ongoing studies in topology and geometry. The CMS is proud to honour Dr. Murphy with the 2025 Krieger-Nelson Prize.
Read more about the award