Noether Profiles

Georgia Benkart

posted Apr 5, 2014, 10:46 AM by AWM Web Editor

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.

Raman Parimala

posted Mar 2, 2013, 8:34 PM by AWM Web Editor   [ updated Mar 3, 2013, 5:35 AM ]

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.

Parimala received her Ph.D. from the University of Mumbai (1976). She was a professor at the Tata Institute of Fundamental Research in Mumbai for many years before moving in 2005 to Emory University in Atlanta, Georgia. She has also held visiting positions at the Swiss Federal Institute of Technology (ETH) in Zurich, the University of Lausanne, University of California-Berkeley, University of Chicago, Ohio State, and the University of Paris at Orsay.
Parimala has won many awards in recognition of her accomplishments.  She gave a plenary address at the 2010 International Congress of Mathematicians (ICM) in Hyderabad and a sectional address at the 1994 ICM in Zurich. By 1992 she was a  Fellow of the Indian Academy of Sciences, the Indian National Science Academy and the National Academy of Sciences India.  In 2005, she was awarded the prize in mathematics by the Academy of Sciences for the Developing World, making her the first woman to receive that honor. Parimala has also received the Srinavasa Ramanujan Medal of the Indian National Science Academy in 2006, an honorary doctorate from the  University of Lausanne in 1999, and the Bhatnagar prize in 1987.

In the seventies, Parimala's examples of nontrivial quadratic spaces over an affine plane came as a surprise to experts in contrast to the affirmative solution of Serre's question on triviality of algebraic vector bundles over an affine space by Quillen and Suslin. Parimala is perhaps best known for proving Serre's Conjecture II for classical groups (Bayer-Fluckiger & Parimala, 1995). This well-known conjecture on the Galois cohomology of linear algebraic groups was formulated in the early 1960s.  The problem is of continued interest and has yet to be solved for many exceptional groups.  Another of her significant contributions to the theory of quadratic forms concerns the u-invariant of a field‚ a measure of the maximum dimension of an anisotropic quadratic form over that field. In a 2010 paper, Parimala proved that the u-invariant of a function field of  a nondyadic p-adic curve is exactly 8, settling a conjecture made nearly 30 years earlier (Parimala & Suresh, 2010).

Carolyn S. Gordon

posted Dec 6, 2010, 11:16 AM by AWM Web Editor   [ updated Dec 6, 2010, 11:24 AM ]

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.

Fan Chung Graham

posted Jul 9, 2010, 10:16 AM by Glenna Buford

New Directions in Graph Theory

Washington, D.C. 2009

FAN CHUNG is an exceptionally productive and influential world-class scholar whose impact has been felt in the classroom, the academy, and the corporate world. Her research interests are primarily in graph theory, combinatorics, and algorithmic design, in particular, in spectral graph theory, extremal graphs, graph labeling, graph decompositions, random graphs, graph algorithms, parallel structures and various applications of graph theory in Internet computing, communication networks, software reliability, and various areas of mathematics and the natural sciences. She has recently been conducting a mathematical analysis of PageRank, a new and important graph invariant concerning correlations between vertices in a graph.

Dr. Chung has made significant contributions to several fields. In combinatorics she has conducted important research in counting Baxter permutations, determining sharper bounds for various Ramsey numbers, in creating, with Ronald L. Graham, the theory of quasi-random combinatorial objects, and in many other areas. In graph theory she has notable results concerning Steiner trees, and a whole sequence of papers, partly with S. T. Yau, concerning the Laplacian of a graph and its significance and properties and implications. Recently she has been interested in the graph-theoretic structure of the Internet, and specifically of the World Wide Web. In that area she has found a number of graph-theoretic statistics and some arresting connections with the Riemann zeta function.

Professor Chung currently holds the positions of Professor of Mathematics, Professor of Computer Science and Engineering, and Akamai Professor in Internet Mathematics at the University of California, San Diego. She was formerly the Class of 1965 Professor of Mathematics at the University of Pennsylvania. For the 20 years following her doctoral studies, she held research positions at Bell Labs and Bellcore, where she headed the Mathematics, Information Sciences and Operations Research Division and directed research groups in combinatorics, algorithms, cryptography, and optimization. At Bell, Fan met and collaborated with many research scientists and mathematicians, including Ronald L. Graham who was to become her husband. At Bell, Fan developed and honed her talent for making connections with seemingly disparate areas of mathematics and the sciences and with the practitioners of those disciplines. She visited Harvard University in 1991 as a Bellcore Fellow and a few years later returned to academia.

Dr. Chung has been awarded numerous honors and awards for her groundbreaking work in spectral graph theory, discrete geometry, algorithms, and communications networks. She has written over 240 papers with about 120 coauthors. Dr. Chung has written 3 books: Spectral Graph Theory, Complex Graphs and Networks (with Lincoln Lu) and Erdös on Graphs (with Ronald L. Graham). She has been a fellow in the American Academy of Arts and Sciences since 1998, an invited speaker at the International Congress of Mathematicians in Zürich (1994), and the recipient of the Mathematical Association of America Allendoerfer Award for expository excellence for her article "Steiner Trees on a Checkerboard" co-authored with Martin Gardner and Ronald L. Graham (1990). She is a magnet for very bright students at UCSD, and has frequently published joint research with them.

The daughter of an engineer, Fan grew up in Kaoshiung, Taiwan. She received a B.S. degree in mathematics from National Taiwan University in 1970 and her Ph.D. in mathematics from University of Pennsylvania in 1974 under Herbert Wilf who directed her thesis entitled "Ramsey Numbers in Multi-Colors."

Audrey A. Terras

posted Jul 9, 2010, 10:14 AM by Glenna Buford

Fun with Zeta Functions of Graphs

San Diego, California 2008

AUDREY TERRAS is a fellow of the American Association for the Advancement of Science and has served on that organization's mathematics section nominating committee. She has served on the Council of the American Mathematical Society and various AMS committees and was an editor of the Transactions of the AMS. Currently she is an associate editor of book reviews for the Bulletin of the AMS and the chair of the Western Section Program Committee. She has served on various AWM committees in the past.

She has written three books: Harmonic Analysis on Symmetric Spaces and Applications, Vols. I, II, Springer-Verlag, New York, 1985, 1988 and Fourier Analysis on Finite Groups and Applications, Cambridge University Press, Cambridge, 1999. She also co-edited, with Dennis Hejhal and Peter Sarnak, the proceedings from a 1984 conference on Selberg's trace formula. Her research interests include number theory; harmonic analysis on symmetric spaces and finite groups along with its applications; special functions; algebraic graph theory, especially zeta functions of graphs; and Selberg's trace formula.

Current research involves finite analogues of the symmetric spaces of her Springer-Verlag volumes. This led her to work on spectra of graphs and hypergraphs attached to finite matrix groups, also coverings of graphs and their zeta and L-functions. These functions are analogues of the Riemann and Selberg zeta functions.

Karen Vogtmann

posted Jul 9, 2010, 10:11 AM by Glenna Buford

Automorphisms of Free Groups, Outer Space and Beyond

New Orleans, LA 2007

Inspired to pursue mathematics by an NSF summer program for high school students at the University of California, Berkeley, KAREN VOGTMANN received both her undergraduate and graduate degrees from Berkeley, investigating algebraic K-theory with Jack Wagoner. After wandering the academic world from Michigan to Brandeis, Columbia to the Institute for Advanced Studies, and back, she settled at Cornell University where she has been for the last twenty years. A profound mathematician, she has authored numerous articles, mentored eight PhD students, and averaged ten invited talks a year. Vogtmann has served as Vice President of the American Mathematical Society and on scientific advisory boards of the American Institute of Mathematics, the Mathematical Sciences Research Institute, the arXiv advisory board, the National Academy of Sciences Delegation to the International Mathematical Union General Assembly, and the Vietnam Education Foundation Panel for mathematics.

 Vogtmann’s research views groups as symmetries of geometric objects. By understanding the geometry and topology of suitably chosen objects, she deduces algebraic information about the groups acting on them. Her work investigates orthogonal and symplectic groups, SL(2) of rings of  imaginary quadratic integers, groups of automorphisms of free groups, and mapping class groups of surfaces. Vogtmann’s recent focus has been on the group of outer automorphisms of a free group where the appropriate geometric object is called Outer Space. This space turns out to have surprising connections with other areas of mathematics, for example with certain infinite-dimensional Lie algebras and even with the study of phylogenetic trees in biology.

Ingrid Daubechies

posted Jul 9, 2010, 10:06 AM by Glenna Buford

Mathematical Results and Challenges in Learning Theory

San Antonio, Texas 2006

INGRID DAUBECHIES grew up in Belgium and received both her bachelor's and Ph.D. degrees (in 1975 and 1980) from the Free University in Brussels. As far as she can remember, she was always interested in mathematics and how things worked, and from an early age, was encouraged by her father, a civil mining engineer, and her mother, a criminologist, to pursue her interest in science. Although she studied to become a physicist, her work has always been very mathematical.

Daubechies held a research position at the Free University until 1987. From 1987 to 1994 she was a member of the technical staff at AT&T Bell Laboratories, during which time she took leaves to spend six months (in 1990) at the University of Michigan, and two years (1991-1993) at Rutgers University. She is now a professor in the Department of Mathematics, the first woman to hold that position, and in the Program in Applied and Computational Mathematics at Princeton University. Her research interests have focused on the mathematical aspects of time-frequency analysis, in particular wavelets, as well as applications. In 1987 she constructed a class of wavelets that were identically zero outside a finite interval, now among the most common type of wavelets used in applications. Currently, she is applying her techniques to learning theory.

Daubechies has received many awards in recognition of her groundbreaking work. In 1984, she received the Louis Empain Prize in Physics, awarded once every five years to a Belgian scientist on the basis of work done before the age of 29. In 1998, she was elected to be a member of the National Academy of Sciences and a Fellow of the Institute of Electrical and Electronics Engineers. The American Mathematical Society awarded her a Leroy P. Steele prize for exposition in 1994 for her book Ten Lectures on Wavelets, as well as the 1997 Ruth Lyttle Satter Prize for "her deep and beautiful analysis of wavelets and their applications." In 2000, she became the first woman to receive the National Academy of Sciences Award in Mathematics, presented every four years, for excellence in published mathematical research. From 1992 to 1997 she was a fellow of the John D. and Catherine T. MacArthur Foundation. She is a member of the American Academy of Arts and Sciences, the American Mathematical Society, the Mathematical Association of America, the Society for Industrial and Applied Mathematics, and the Institute of Electrical and Electronics Engineers.

Daubechies has been very involved in helping communicate mathematics to the public, in particular in coming up with ideas for the K-12 mathematics curriculum that reflect present-day applications of mathematics. Her husband is also a mathematician, and they have two children, Michael and Carolyn. When she is not working or asleep, she likes to spend time with her family.

Lai-Sang Young

posted Jul 9, 2010, 10:01 AM by Glenna Buford

From Limit Cycles to Strange Attractors

Atlanta, Georgia 2005

LAI-SANG YOUNG was born in Hong Kong and emigrated to the United States to pursue higher education in mathematics at the University of Wisconsin, Madison (B.A., 1973) and the University of California, Berkeley (M.S., 1976; Ph.D., 1978). She published her first paper as a graduate student in 1977, and conducted doctoral research under the direction of Robert Bowen; resulting a dissertation, entitled Entropy and Symbolic Dynamics of Certain Smooth Systems. She began her illustrious academic career at Northwestern University, and in 1980, moved to Michigan State University where she was promoted to Associate Professor in 1984. She then moved to the University of Arizona in 1987, where she became Professor of Mathematics in 1990, spent nine years at UCLA, and in 1999 joined NYU's Courant Institute of Mathematical Sciences. She visited the University of Warwick in England, the Mathematical Sciences Research Institute at Berkeley, Universitat Bielefeld in Germany, the Institute for Advanced Study at Princeton, and the College de France, among others.

Lai-Sang Young has done pioneering work on dynamical systems. Her interests in geometric ergodic theory include applications, and connections to probability and mathematical physics. Chaotic dynamical systems are her specialty; the main themes of her research interests are measurements of dynamical complexity, strange attractors, cumulative effects of small random perturbations ("noise") on long term behavior of dynamical systems, and probabilistic laws for chaotic systems. Lai-Sang has authored or co-authored over 50 scholarly publications as well as numerous expository articles, and has been an invited plenary lecturer for meetings of the AMS, SIAM, and IMA, as well as for the ICM, and ICMP (International Congress of Mathematical Physics). Her work has been supported by the National Science Foundation from 1979 to the present, and has garnered wide respect and acclaim. In 1985, she was awarded an Alfred P. Sloan Foundation Fellowship, an award reserved for individuals within six years of earning the Ph.D. who demonstrate "the most outstanding promise of making fundamental contributions to new knowledge". In 1993 she was awarded the Ruth Lynn Satter Prize for sustained outstanding research contributions over a five-year period by a female mathematician. She was awarded in 1997 a Guggenheim Foundation Fellowship, and was elected in 2004 as a Fellow of the American Academy of Arts and Sciences, "an international learned society composed of the world's leading scientists, scholars, artists, business people, and public leaders".

In response to the presentation of the Ruth Lynn Satter Prize over a decade ago, Lai-Sang Young poignantly recognized the gains as well as the obstacles for women in mathematics, and her comments are just as relevant today: "There is no doubt that our situation has improved; life in academia for women is easier for my generation than the generation before. I feel that more institutional support is still needed for women who try to juggle career and family, and a conscious effort on our part is necessary if we are to rid ourselves of the cultural prejudices that have existed for so long."

- 2004 AWM Noether lecture planning committee: Debra Warne (chair), Lenore Blum, Irwin Kra

Svetlana Katok

posted Jul 9, 2010, 9:57 AM by Glenna Buford

Symbolic dynamics for geodesic flows

Phoenix, Arizona, 2004

SVETLANA KATOK grew up in Moscow in an environment saturated by mathematics: family, mathematical circles at the university, special mathematical schools, mathematical olympiads. She was especially influenced by her father Boris Rosenfeld, a renowned geometer and one of the most distinguished historians of science in the world. At the early age of thirteen, she decided to become a professional mathematician. She earned an M.A. with honors from Moscow State University in 1969. Her first published paper, based on her master's thesis, was reviewed by Jurgen Moser. However, due to the anti-Semitic and anti-intelligentsia policies of the time, she was denied admission to the university Ph.D. program and worked for several years in the area of early and secondary mathematical education.

After emigrating to the United States in 1978, she returned to research mathematics and entered the Ph.D. program at the University of Maryland. She changed her research area from dynamical systems to number theory and completed her degree under Don Zagier in 1983. She was awarded an NSF postdoc and was associated with Caltech and four campuses of the University of California before moving to Penn State in 1990, where she was promoted to full professor in 1993. Her mathematical interests center on the interaction between number theory, geometry and dynamical systems with the latter field, her first mathematical specialty, coming to the fore in the last decade.

She has a life-long interest in mathematical education, which has borne such diverse fruits as innovative programs for primary school students from the Soviet period, the popular graduate text Fuchsian Groups and the unique MASS program for undergraduates at Penn State that she created together with her husband Anatole Katok. The topics of her many invited talks are quite varied, ranging from her mathematical research to models for integrating research into the undergraduate experience. In 1995 she founded ERA-AMS, the first electronic-only AMS journal, and is managing editor of the journal. She has been a member of the Editorial Board of the Journal of the Institute of Mathematics of Jussieu since 2000. She has served on many AMS, NSF and NRC committees and panels and was a Member-at-Large of the AMS Council for 1993-1996. In 2001 she received the Eberly College of Science Alumni Society Distinguished Service Award.

She has three children whose careers range from operations research to software development and architecture to classical singing.

Jean E. Taylor

posted Jul 9, 2010, 9:55 AM by Glenna Buford

Five Little Crystals and How They Grew

Baltimore, Maryland, 2003

JEAN E. TAYLOR was born and grew up in Northern California as the middle of three children. There were no scientists or mathematicians in her family; her father was a lawyer and her mother a high school gym teacher and counselor. She went to Mount Holyoke College as a "back east" adventure, where she sorely missed the presence of boys but found success and wonderful mentors in the form of two female chemistry professors and a male psychology professor. The Outing Club both connected her to boys and instilled in her a life-long love of hiking in mountains.

She received her A.B. (summa cum laude and first in her class) in 1966 and went to the University of California to study chemistry. After passing her qualifying exams and beginning to work on a thesis that did not inspire her, she audited a class in differential geometry taught by S.S. Chern which did. With his help, she transferred to mathematics (obtaining an M.Sc. in chemistry in the process). Then, overwhelmed by the political turmoil in Berkeley, she went to the University of Warwick where she completed an M.Sc. in mathematics. Finally, she went to Princeton University in fall 1970 and finished her thesis work in May 1972, under the supervision if Fred Almgren. While an instructor at MIT she finished writing her thesis; her Princeton Ph.D. was awarded in January 1973. She is eternally grateful in NSF or supporting her with a Graduate Fellowship throughout six years and four different graduate programs.

In 1973 she went to Rutgers University as an Assistant Professor and rose through the ranks to Professor. in 2002 she became Professor Emerita there and settled into the Courant Institute. Her research has been primarily in the field of Geometric Measure Theory applied to problems of optimal shapes of crystals, both in equilibrium and otherwise. Among her honors are receiving an Alfred P. Sloan Foundation Fellowship and being named a Fellow of the American Academy of Arts and Sciences as well as of the American Association or the Advancement of Science (AAAS) and the Association for Women in Science. In May 2001 she was awarded an honorary D.Sc by Mount Holyoke.

Taylor was President of the AWM from 1999-2001 She has also served the AMS in many capacities, ranging from the Nominating Committee in the 1970s to the Council and then its Executive Committee, to being elected a Vice President and, in fall 2002, a Trustee. She was also a member of the Board of Directors of AAAS. She gave an invited address to the AMS in 1976 and an AMS-MAA invited address in 1989. She was the Hedrick Lecturer for the MAA in 1998 and a plenary speaker at the AMS Mathematical Challenges meeting in August 2000 at U.C.L.A; a paper based on that lecture appears in the January 2003 issue of the Bulletin of the AMS. She has organized meetings and sessions for SIAM and ICIAM as well as for AMS, AWM, and AAAS; she has been a consultant for Project NeXT, a member of the executive committee of CBMS, the AMS Council representative to JPBM, Trustee of Black Rock Forest Consortium, and has held numerous other positions.

Taylor has been married to three extraordinary men: John Guckenheimer, Fred Almgren, and now William T. Golden. She has a daughter and two step children via Almgren, and two more adult stepdaughters via Golden. In her spare time she enjoys hiking (she recently became a member or the Catskill 3500 Club), reading and puzzles of all kinds.

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