Emmy Noether Lectures

2012 Lecturer: Barbara Keyfitz

Conservation Laws – Not Exactly a la Noether

Emmy Noether’s famous theorem connects “conservation laws” with symmetries, and so perhaps the first thing that a speaker should do in a talk bearing her name is to explain that the relation between that theorem and the research area of hyperbolic conservation laws is not very close. That done, I will describe the main features of conservation law theory, beginning with the role of weak solutions (which break symmetry), and elements of the theory in a single space variable, which is now in a reasonably satisfactory state, and concluding with an outline of the current state of the theory for multidimensional conservation laws. Here there are a few results, most of them very recent.
Brief Biography
Barbara Keyfitz is a renowned mathematician who has made important and original contributions to applied mathematics. She has been an outstanding leader of the mathematical community both as a scientist and administrator.
Her research is on nonlinear partial differential equations with emphasis on hyperbolic conservation laws and evolution equations that change type from hyperbolic to elliptic. She had a pioneering role in tackling the most challenging problems in the field, and opened up a new research direction by developing a powerful new technique dealing with free boundary problems to further the understanding of transonic shock. Keyfitz also studied bifurcation problems in reaction-diffusion equations, especially in the theory of shock waves. She succeeded in adapting techniques from vector field dynamics to the problem of the admissibility of shock waves, a long-lasting question in applied mathematics. She is currently developing analytical techniques to confirm Guderley Mach reflection, an unexpected singular behavior seen numerically at the formation points of Mach stems. She has mentored doctoral students and postdoctoral researchers and her co-authors include S. Čanić, M. Golubitsky, B. Grossman, E.H. Kim, H. C. Kranzer, R. E. Melnik, R. Sanders, D. Schaeffer, M. Severs and A. Tesdall.
Professor Keyftiz is the Dr. Charles Saltzer Professor of Mathematics at the Univeristy of Ohio. She was formerly the John and Rebecca Moores Professor of Mathematics at the University of Houston. She was the first woman scientist to receive the Esther Farfel award which is the highest honor the University of Houston bestows on a faculty member. Dr. Keyfitz has also held permanent positions at Columbia, Princeton, Arizona State, and   visiting positions at Berkeley, Brown, Chinese University of Hong Kong , Duke, the Taiwan National Center for Theoretical Sciences, Université de Nice and Université de St Etienne. From July 2004 to December 2008 she was the director of the Fields Institute in Canada.
Dr. Keyfitz has given numerous invited talks on the subject of conservation laws. In 2009, she gave a plenary lecture at the 14th General Meeting of European Women in Mathematics. She was an invited speaker at ICIAM 2007. In 2006 she was a joint plenary speaker at the SIAM Analysis of PDE conference and the SIAM Annual Meeting. She gave the Presidential Address at the 33rd Annual Meeting of the Statistical Society of Canada in 2005.
Dr. Keyfitz has served on the editorial board of the Journal of Mathematical Analysis and Applications, the SIAM Journal of Applied Mathematics and of both Proceedings and Transactions of the American Mathematical Society. She was appointed a Fellow of the AmericanAssociation for the Advancement of Science in 1992, and serves as chair of their mathematics section. Dr. Keyfitz is currently the president of the International Council for Industrial and Applied Mathematics (ICIAM).
Barbara Keyfitz is the daughter of the famous demographer Nathan Keyfitz who worked at Statistic Canada. She was born in Ottawa and did her undergraduate work at the University of Toronto. Her dissertation, titled “Time-decreasing functionals of solutions of nonlinear equations exhibiting shock waves” was directed by Peter Lax and she received her Ph.D. in 1970 from Courant University.
In 2005, Dr. Keyfitz was awarded the Canadian Mathematical Society’s Krieger-Nelson Prize. She has played a prominent role in mentoring women in mathematics and served as the president of the Association for Women in Mathematics from February 2005 to January 2007. By naming her the 2011 Noether Lecturer, the women of mathematics further acknowledge the achievements of this extraordinary woman.