Joan and Joseph Birman Research Prize 2019
The 2019 Joan & Joseph Birman Research Prize in Topology and Geometry is awarded to Kathryn Mann for breakthrough work in the theory of dynamics of group actions on manifolds.
Mann uses a broad array of mathematical tools to obtain results at the juncture of topology, group theory, geometry and dynamics, and she finds new connections between them. She has discovered new phenomena, built general theory, and has solved long-open problems.
As an example, in a solo paper she introduced a new method to study the topology of the space of surface group representations in the space of orientation-preserving circle homeomorphisms and to prove a rigidity result about geometric such representations. Building on this paper, jointly with M. Wolff,
Mann proved that conversely this rigidity property characterizes the geometric surface group actions on the circle. A leading expert describes this as one of the best results obtained in the area in the last couple of decades and another mathematician describes Mann as “that once-in-a-generation thinker who opens significant new directions for research”.
Kathryn Mann received her PhD in 2014 from the University of Chicago. During 2014-2017 she was a Morrey Visiting Assistant Professor and an NSF postdoctoral fellow at the University of California at Berkeley. She now holds a Manning Assistant Professorship of Mathematics at Brown University.
I am very honored to be selected for the Birman research prize, and deeply grateful to Joan and Joseph Birman for their support in establishing the award with the AWM. I had the pleasure of meeting Joan last fall, after many years of knowing her work. I realize now how fortunate I was to “grow up” mathematically in a field in which Joan Birman was a household name.
I’d like to take this opportunity to thank the many mentors I have had — first and foremost my advisor Benson Farb, and the surrounding community at the University of Chicago. It was there that I first encountered the kind of questions in geometry and dynamics that continue to fascinate me. Though too many to list here, I am indebted to all those I have looked up to and who serve as a continuing source of inspiration: mentors, collaborators, and mathematical friends. I’m very grateful also to my current colleagues at Brown for giving me such a warm welcome and an immediate show of support.