Walking on Graphs the Representation Theory Way Baltimore, MD 2014 Georgia Benkart is an international leader in the structure and representation theory of Lie algebras and related algebraic structures. A longtime faculty member at the University of Wisconsin, she received her Ph.D. from Yale in 1974 with Nathan Jacobson. She has given hundreds of invited talks worldwide and published over 100 journal articles, mainly within four broad categories: (1) Modular Lie algebras, (2) Combinatorics of Lie algebra representations, (3) Graded algebras and Superalgebras, and (4) Quantum groups and related structures. Many of her most important papers represent breakthroughs. Her work on the classification of the rank one modular Lie algebras and on the “Recognition Theorem” provided the building blocks for the subsequent classification of the finite-dimensional simple modular Lie algebras. The combinatorial tools developed in other papers provided an effective way to study the stability of root and weight multiplicities of finite dimensional as well as infinite dimensional Kac-Moody Lie algebras. Motivated by the creation and annihilation operators in physics, Benkart and Roby introduced a new family of algebras, "down-up algebras" that still inspire current research. Benkart and co-authors introduced crystal bases for representations of general linear quantum superalgebras, and in a series of papers, she, jointly with others, determined the Lie algebras graded by finite root systems. Georgia has given excellent service to the mathematical community, particularly as a former President of AWM and as current AMS Secretary. She has been a superb mentor for her 21 Ph.D. students and postdocs. She won the University of Wisconsin Distinguished Teaching Award in 1987 and the Mid-Career Faculty Research Award in 1996. A fantastic speaker, Georgia was the Mathematical Association of America Polya Lecturer for 2000-2002. |
San Diego, CA 2013 Raman Parimala is the Arts and Sciences Distinguished Professor of Mathematics at Emory University and has been selected as the 2013 Noether Lecturer for her fundamental work in algebra and algebraic geometry with significant contributions to the study of quadratic forms, hermitian forms, linear algebraic groups and Galois cohomology. |
You Can’t Hear the Shape of a Manifold
San Francisco, CA 2010 Carolyn S. Gordon is the Benjamin Cheney Professor of Mathematics at Dartmouth College and was selected as the 31st Noether Lecturer because of her fundamental contributions to inverse spectral problems. Gordon received her B.S. and M.S. in Mathematics from Purdue University and her Ph.D. from Washington University. She began her career as the Lady Davis Postdoctoral Fellow at Technion Israel Institute of Technology, followed by positions at Lehigh University and Washington University before joining the Dartmouth faculty in 1992. Gordon's papers have appeared in diverse settings - from research journals to popular journals such as the Intelligencer. She was awarded a Centennial Fellowship by the American Mathematical Society in1990. She and David Webb received the Chauvenet Prize from the Mathematical Association of America in 2001 for their 1996 American Scientist paper, "You can't hear the shape of a drum." Gordon has given numerous seminars and colloquia at universities throughout the world. She was the principal speaker at the Conference Board on Mathematical Sciences conference “Advances in Inverse Spectral Geometry” in 1996. She has been an AMS Invited Speaker at the Joint Mathematics Meetings and an AMS-MAA Invited Speaker at MathFest. She is a member of the editorial board of the Journal of Geometric Analysis and the Korean Mathematics Journal. Gordon is a Past President of the Association for Women in Mathematics and continues to be a very active member. Many mathematicians will know her as the organizer of the AWM January workshops, a role she held for a number of years. She is currently a member of the AWM Policy and Advocacy Committee. Gordon is a former member of the Executive Council of the Conference Board on Mathematical Sciences and has held elected positions on the Editorial Boards Committee and the Council of the American Mathematical Society. She has served on many AMS committees including the Committee on the Profession, and the Committee on Committees. Gordon's research interests are in Riemannian geometry with emphasis on inverse spectral problems and on the geometry of Lie groups. Mark Kac's question “Can one hear the shape of a drum?” asks whether the eigenvalue spectrum of the Laplacian on a plane domain determines the domain up to congruence. Gordon is particularly well-known for her work on this question and its analog for more general Riemannian manifolds. Among her constructions are the first examples of domains with the same eigenvalue spectrum (joint work with David Webb and Scott Wolpert) and continuous families of isospectral Riemannian metrics on spheres. |