Lia Bronsard is one of Canada’s leading mathematical analysts, whose interests lie in the field of partial differential equations and the calculus of variations. She specializes in the study of singular limits of solutions of partial differential equations. Her research brings rigorous methods of analysis to bear on problems arising in the physical sciences, and in particular those involving singular geometrical structures such as vortices, phase transition layers, and grain boundaries.
Bronsard was born in Québec in 1963 and received her Baccalauréat ès sciences in mathematics from the Université de Montréal in 1983. She received her Ph.D. in 1988 from the Courant Institute of Mathematical Sciences at New York University, working with R. V. Kohn on the De Giorgi conjecture connecting singularly perturbed reaction-diffusion equations and mean curvature flow. After her degree, she held positions at Brown University, the Institute for Advanced Study, and the Center for Nonlinear Analysis at Carnegie Mellon University. In 1992, she moved to McMaster University, where she is now a Professor of Mathematics.
During the period after her thesis, Bronsard worked on energy driven pattern formation in collaboration with B. Stoth and others. Her paper with F. Reitich on the structure of triple-junction layers in grain boundaries, from her period at CMU, was the first mathematical analysis of these multiphase singular structures and has been highly influential.
In her current research, Bronsard studies the detailed structures of vortices in the phenomenon of Bose-Einstein condensation and in the Ginzburg-Landau models of superconductivity. In this area, her work, in collaboration with S. Alama, T. Giorgi, P. Mironescu, E. Sandier and colleague J. Berlinsky from Physics at McMaster University, sets a very high standard of quality, and is a model of interdisciplinary research.
She is president of the Canadian Mathematical Society for the 2014-2016 term.