My father was an engineer and was good in mathematics. My mother was a successful teacher at all levels from kindergarten through to college. She majored in English, biology, and education.

My parents encouraged our educational activities but didn't try to influence the subjects we studied. I started out wanting to become a chemist but soon found I was allergic to most things in the lab including the work.

I always have loved science and mathematics and remember joining the science club as soon as I could.

Participating in a summer program for high school students at Hiram College awakened Georgia's self-confidence in her intellectual abilities.

The honours mathematics program at Ohio State University was the determining factor in my becoming a mathematics major. We were treated to small classes and excellent teachers who encouraged us to take graduate courses when they thought we could do well in them. Professors Joan and Jim Leitzel and Joe Ferrar stimulated my interest in abstract algebra with challenging courses, and I remember quite fondly a graduate p-adic analysis course I took when I was a junior from the famous number theorist Kurt Mahler.

This paper is intended to improve the theory of Moore-Smith Convergence by generalising the definition of subnet.

As a graduate student, I took a course in Lie algebras from the group theorist Walter Feit. Even though there were experts in Lie theory on the faculty at Yale, he was teaching the course that term because he wanted to study the subject. So we all struggled to learn the topic together, and that is how I became interested in Lie algebras.

This dissertation presents a systematic investigation of the role of inner ideals in the study of Lie algebras. The elementary properties of inner ideals obtained give a classification of minimal inner ideals. As a result of this classification a Lie algebra which has minimal inner ideals is shown to have ad-nilpotent elements unless every minimal inner ideal is a simple ideal which has no proper inner ideals. On the other hand the existence of ad-nilpotent elements implies the existence of non-trivial inner ideals. We investigate Lie algebras which satisfy the minimum condition on inner ideals and contain non-zero ad-nilpotent elements. Such a Lie algebra decomposes into the direct sum of copies of a Jordan algebra, copies of a Jordan bimodule, and a Lie subalgebra of derivations of the Jordan algebra and bimodule. The main feature of this decomposition is the correspondence between the Lie and the Jordan structures. As a consequence of the Jordan structure theory necessary and sufficient conditions can be given for the Lie algebra to be the direct sum of a finite number of simple Lie algebras which satisfy the minimum condition on inner ideals.

Many people have contributed to my mathematical education. I owe them all my sincerest thanks. I would like to express my special appreciation to my advisor, Professor Nathan Jacobson, and to Professor George Seligman who first suggested inner ideals as a possible avenue of research.

Shortly after Georgia Benkart arrived at the University of Wisconsin Madison, she gave a graduate course in Lie algebras. I attended Georgia's lectures in this course, and I was doubly impressed. First, although I had seen Lie algebras previously, I not realised how beautiful that subject could be until Georgia made it come alive in her course. In fact, I was nearly seduced by Georgia's lectures into abandoning my first mathematical love - group theory - and I began thinking about problems in Lie algebras. Indeed, I wrote and published two papers (jointly with Georgia and our colleague, J Marshall Osborn) on simple Lie algebras in prime characteristic, and a further paper jointly with Georgia. Another impressive aspect of Georgia's course was her beautiful lectures. These were carefully prepared and extremely well presented, and even her blackboard use was exceptionally fine, with beautiful handwriting and excellent organisation. I also got to know Georgia very well in a non-mathematical context. She lived for a while in an apartment building adjacent to where I lived, and since I had a very convenient campus parking space, we agreed that she would come to the mathematics department each morning in my car. Because of this daily contact, our friendship developed nicely. I enjoyed those commutes with Georgia, and I was sad when she moved out of my neighbourhood, and thus ended our morning co-commutes.

In the fall of '79, I was a timid graduate student, and had been late getting started on a thesis. Either the day she was awarded tenure or the day after, with considerable apprehension, I approached her office, just a couple of doors down from my own, to ask her whether I could work with her. She immediately put me at ease and took me on as a student. I was extremely fortunate she did so because she was all you could expect of an advisor, and many times more. I am indebted to her for being such a wonderful mentor, and also for introducing me to a beautiful subject and its many connections with other parts of mathematics and physics.

... told in Dickensian fashion the story begun 80 years ago by Issai Schur tying the knot between the symmetric groups and the general linear groups of invertible matrices. It's a old story but nevertheless a very timely one with many new developments and applications to the theory of symmetric functions, representation theory, knot theory, invariant theory, combinatorics, and particle physics. An expanded version of this talk was the basis of her 10 lectures at Holiday Symposium at New Mexico State University in December 1992.

Each year the Board of Governors of the Mathematical Association of America selects a Pólya Lecturer, to serve for two academic years. Georgia Benkart has been selected to serve in 2000-01 and 2001-02. On a rotating basis, the various MAA sections around the country can invite a current Pólya Lecturer (there are two at any given time) to speak at a regional meeting. ... She is regarded as an inspiring and dedicated teacher, in the best traditions of George Pólya ... Giving lectures around the country won't be anything new for Georgia. In the year 2000 she gave 9 invited lectures, including lectures at MSRI (Berkeley), Seoul National University (Korea), Canada (Toronto and Alberta), and Oberwolfach (Germany). In 1999 among her 11 invited lectures were the Taft Lectures at the University of Cincinnati. Professor Benkart currently serves on the editorial boards of the 'Journal of Algebra' and the 'Korean Mathematical Colloquium'.

There is a simple matching between n × n patches of square ice with certain boundary conditions and n × n alternating sign matrices, which in turn have many beautiful connections with a host of other topics - domino tilings, tableaux, determinants, symmetric functions and group characters. This talk will journey through many of these topics.

How many walks of n steps are there from point A to point B on a graph? Often finding the answer involves clever combinatorics or tedious treading. But if the graph is the representation graph of a group, representation theory can facilitate the counting and provide much insight.

The ICM Emmy Noether lecture honours women who have made fundamental and sustained contributions to the mathematical sciences.

The McKay correspondence and Schur-Weyl duality have inspired a vast amount of research in mathematics and physics. The McKay correspondence establishes a bijection between the finite subgroups of the special unitary 2-by-2 matrices and the simply laced affine Dynkin diagrams from Lie theory. It has led to the discovery of many other remarkable A-D-E phenomena. Schur-Weyl duality reveals hidden connections between the representation theories of two algebras that centralise one another in their actions on the same space. We merge these two notions and explain how this gives new insights and results. Our approach uses the combinatorics of walks on graphs, the Jones basic construction, and partition algebras.

... demonstrated a sustained commitment to the support and advancement of women in the mathematical sciences, consistent with the AWM mission: "to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity and the equal treatment of women and girls in the mathematical sciences."

Georgia Benkart is a leader in the representation theory of Lie algebras and Kac-Moody algebras with fundamental contributions to several branches of Lie Theory. In a series of joint papers with Osborn, she classified simple modular Lie algebras of toral rank one which proved to be a crucial building block for the classification of simple modular Lie algebras. Together with Britten and Lemire, she made important contributions to stability questions in combinatorial representation theory, a topic getting lots of attention recently. In a joint paper with E Zelmanov, she found a highly nontrivial description of all root graded Lie algebras, which provided the key idea for really getting control of root graded Lie algebras. More recently, Benkart, Kang and Kashiwara constructed nice crystal bases for general linear Lie superalgberas, a highly nontrivial piece of work. Besides her deep contributions in mathematics, she has been a very successful mentor with more than twenty Ph.D. students. She has contributed profusely to mathematics through her services as office bearer at the AMS as well as AWM.

... we feel that Georgia's contribution to our discipline goes well beyond this astonishing catalogue of research papers, monographs, lectures, and service roles. She has left an indelible mark on a generation of mathematicians through supportive collaborations with more than 90 co-authors, many of whom are (or, more accurately, were) early-career researchers. And there are even more mathematicians who were not her co-authors but for whom Georgia's mentoring, advice, and support made it possible for them to achieve much more than they ever expected of themselves. Georgia, always humbly and perfectly, serves as a role model and mentor to all.

Georgia Benkart was stunned to learn on Wednesday, April 27, that the pain and fatigue she had been fighting through to fulfil her professional commitments came from an illness that was about to take her life. It did so two days later.

I have known Georgia Benkart ever since I came to the department in 1985. Over the years, I saw Georgia deal with problems large and small. And somehow, once Georgia got involved, the problem was solved in less time than expected. To be sure, Georgia was profoundly competent and well organized. But that description alone does not do her justice. For Georgia, a project was not just about getting it right; it was also about making it beautiful. I have read many of Georgia's mathematical papers. Each paper was a polished gem, that would make any lawyer or poet proud. I attended many of Georgia's lectures at conferences and seminars. Each lecture was a work of art, that engaged the audience from beginning to end. I attended many a faculty meeting during which Georgia got up to speak. Invariably, what she said was so well polished and delivered, that it reminded me of Lincoln's Gettysburg address.

I am incredibly lucky to have known Georgia as my teacher, advisor, collaborator, and friend. It is nearly impossible to describe how important she has been to me or to imagine how differently things may have turned out for me had I not known her. Georgia was kind, brilliant, patient, generous, and extremely funny, and I wish I could still remember all of the many times she exhibited those traits. She was also remarkably thorough. I was lucky enough to have collaborated with Georgia several times, and I can vividly recall the first time I wrote a paper with her. At a certain point, we had proved some nice theorems and had written rigorous proofs of those theorems. I thought we were close to being able to submit our paper. I could not have been more wrong. We subsequently engaged in a process of proofreading that was unlike anything I had ever done, and after many many many more drafts, we had a paper of which I am still proud. I like to imagine that if Georgia were to read this remembrance, she would suggest a few small wording changes that would greatly improve it. I miss her very much.