# The Joan and Joseph Birman Research Prize in Topology and Geometry of the AWM

The Association for Women in Mathematics established the Joan and Joseph Birman Research Prize in Topology and Geometry in 2013. First presented in 2015, this prize is awarded every odd year to a woman early in her career who has published exceptional research in topology/geometry. The area topology/geometry is broadly interpreted to include topology, geometry, geometric group theory and related areas. Candidates must be women working at a US institution either within ten years of being awarded a Ph.D., or not being tenured at the time of application. The website of the Association for Women in Mathematics states:-
The Association for Women in Mathematics Joan & Joseph Birman Research Prize in Topology and Geometry serves to highlight to the community outstanding contributions by women in the field and to advance the careers of the prize recipients. The award is made possible by a generous contribution from Joan Birman whose work has been in low dimensional topology and her husband Joseph who is a theoretical physicist whose specialty is applications of group theory to solid state physics.
We give below winners of the prize and also the citation and the reply from the winner.

Winners of the Joan and Joseph Birman Research Prize in Topology and Geometry:

2015 Eli Grigsby, Boston College.

Citation: The inaugural 2015 Joan & Joseph Birman Research Prize in Topology and Geometry is awarded to J Elisenda Grigsby in recognition of her pioneering and influential contributions to low-dimensional topology, particularly in the areas of knot theory and categorified invariants. Her research has centred on the interplay between the combinatorial theory of Khovanov homology and the more geometric Heegaard-Floer homology. World leaders in the field have praised her fundamental contributions, noting that her work both connects and unifies structures in geometric, symplectic, and contact topology, homological algebra, and representation theory. To single out just one of her many outstanding results, she and her collaborator Wehrli discovered that Khovanov's categorification of the $n$-coloured Jones polynomial detects the unknot when $n > 1$. This work has generated a great amount of excitement and activity in the field and was described by a leading expert as "one for the history books". Eli Grigsby is a talented young mathematician who has established herself as a leader in a rapidly developing area that changed the landscape of low-dimensional topology. She was the recipient of an NSF postdoctoral fellowship and DMS research grant, and currently holds an NSF CAREER award. She has a track record of impressive results, and she has provided leadership in her field. Grigsby clearly merits the distinction of being the first mathematician to receive the Joan and Joseph Birman Research Prize in Topology and Geometry.

Response from Eli Grigsby: I am deeply honoured to be receiving this award, especially since Joan Birman is a personal hero of mine. Her work laid the foundations for much of my own; the field of low-dimensional topology would be far poorer without her contributions. Her mathematical accomplishments are particularly impressive in light of the fact that she received her PhD only after a 15-year detour in industry, during which she also had 3 children. She is without question one of the most amazing people I have ever known. Many thanks to the Association for Women in Mathematics, not only for establishing this award, but also for connecting me to a whole community of women whose mathematics and life-stories are similarly inspiring. I am profoundly grateful as well to Joan and Joseph Birman for the thoughtfulness and generosity they exhibited in endowing this award. Of course, I am forever in debt to my tirelessly supportive advisors, Rob Kirby and Peter Ozsváth, along with the rest of my extended mathematical "family." Finally, I would like to thank my colleagues at Boston College, both for their nomination and for making the BC math department such an exciting place to learn and do mathematics.

2017 Emmy Murphy, Massachusetts Institute of Technology.

Citation: The 2017 Joan & Joseph Birman Research Prize in Topology and Geometry is awarded to Emmy Murphy for major breakthroughs in symplectic geometry. Murphy has developed new techniques for the study of symplectic and contact structures on manifolds, uncovering a startling degree of flexibility in a branch of geometry that is ordinarily distinguished by rigidity. As a result, some geometric problems can now be reduced to homotopy theory; for example Murphy's methods have yielded answers to long-standing questions concerning the existence of contact structures on high-dimensional manifolds. She has shown great creativity in the delicate work of inventing powerful new $h$-principle techniques. She has also masterfully combined these new tools with other tools, such as the method of pseudo-holomorphic curves, to explore the boundary between flexibility and rigidity. Murphy is a highly original thinker, and leading geometers will not be surprised if she goes on to make breakthroughs in very different areas of mathematics.

Response from Emmy Murphy: I am very honoured to be a recipient of the Joan & Joseph Birman Prize. My work would never have been possible without my many mentors, particularly Chris Herald, Alex Kumjian, Tom Mrowka, and Paul Seidel. I would also like to thank my collaborators for stimulating and inspiring ideas, particularly Strom Borman, Roger Casals, Baptiste Chantraine, Mike Freedman, and Fran Presas. Yasha Eliashberg deserves special mention, as a wonderful advisor, collaborator, and friend. I'd like to thank Joan and Joseph Birman for being so generous and supportive of the women in mathematics community. Joan Birman is certainly an inspiration to me.
There are many people in mathematics who deserve my warmest thanks, but cannot be listed here. And of course, I'd like to thank my family and friends for their love and support. Finally, I'm grateful to the selection committee for the recognition of my work, and the kind words. I have always had an appreciation for highly visual and geometric questions, and I'm very happy to find places where this kind of thinking is useful. Symplectic and contact geometry, though very fashionable, are still very young fields. And though we've developed a lot of machinery in recent years, there are still many basic questions we don't know the answer to, and I believe many deep theorems can still be proven from first principles. I'm very excited to see where the field will go in upcoming years.

2019 Kathryn Mann, Brown University

for "major breakthroughs in the theory of dynamics of group actions on manifolds"