Georgia Benkart, Emeritus Professor of Mathematics at UW-Madison, died unexpectedly on April 29 in Madison, Wisconsin, leaving behind a worldwide network of colleagues and former students who considered her not only a gifted mathematician, but also a dear friend and mentor. Benkart, who joined the UW-Madison math department in 1974 after earning her PhD from Yale University, was the second woman to join the department.
Originally from Youngstown, Ohio, Georgia Benkart attended Ohio State University for her undergraduate education and received her PhD from Yale University in 1974 under Professor Nathan Jacobson. She retired as a full professor in 2006.
“Georgia Benkart was internationally known for her contributions to mathematics, hugely popular among graduate students, and a really good friend,” says Gloria Mari-Beffa, former chair of the Department of Mathematics and now Associate Dean for the Natural, Physical and Mathematical Sciences in the College of Letters & Science. “Her impact continued to resonate in the math department long after her retirement. There are so many of us who were deeply touched by her. It is a great loss.”
Mari-Beffa points to a recent tribute to Benkart from the American Mathematical Society, “Gems from the Work of Georgia Benkart,” by former colleagues Tom Halverson (Macalester College) and Arun Ram (University of Melbourne), as an excellent summation of Benkart’s body of work.
Paul Terwilliger, Professor of Mathematics and a colleague of Benkart’s since 1985, remembers her elegant problem-solving abilities.
“To be sure, Georgia was profoundly competent and well organized,” he says. “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. Each of her papers was a polished gem, that would make any lawyer or poet proud. Each lecture was a work of art, that engaged the audience from beginning to end.”
Professor Benkart made many important contributions around the study of Lie algebras, structure of algebras, quantum groups, representation theory and combinatorics. Her work with UW-Madison Professor Emeritus Marshall Osborn and others in the 1970s and 1980s was fundamental in the classification of simple Lie algebras. In the 1990s she made numerous contributions in combinatorial representation theory (with significant joint papers with her graduate students) and in the structure and classification of root system graded Lie algebras. Bruce Allison, Yun Gao, Efim Zelmanov and others collaborated with her in this work.
“Georgia and Marshall Osborn brought me to Madison and guided me in my new American life,” says Zelmanov, who was a professor of mathematics at UW-Madison from 1990-1994 and was awarded the prestigious Fields Medal in 1994. “Think how lucky I was, to have such guides! Georgia has always been literally an angel, with an incredible sense of humor and a lot of down-to-earth common sense. I still quote her on many occasions.”
As her career built momentum, Benkart continued with contributions in quantum groups and crystals (with Seok-Jin Kang, Masaki Kashiwara, Paul Terwilliger and others) and in elemental algebras and deformation theory of algebras (with Tom Roby, Sarah Witherspoon and others).
“Georgia’s research program always had many projects on many burners,” says Arun Ram, Professor of Mathematics at the University of Melbourne, who worked alongside Benkart at UW-Madison from 1999-2007. “Her impact as a mentor to young researchers, graduate students and the community of women in mathematics was one of her greatest contributions. So many younger-generation mathematicians have benefited from the capability and inspiration that they received from Georgia’s mentorship and support.”
As the global community became more connected, Benkart led groups of early-career researchers on projects at Banff International Research Station, Mathematical Sciences Research Institute (MRSI), and the Institute for Advanced Study. Two highlights from the last few years of Georgia’s research are her work on walks and dynamics from multiplying representations, with Persi Diaconis, Tom Halverson, Martin Liebeck, Pham Tiep and others, and her work on tensor representations and Mackay quivers with WINART (Women in Noncommutative Algebra and Representation Theory) research groups.
Chelsea Walton, Associate Professor of Mathematics at Rice University and one of the founders, along with Georgia Benkart and Ellen Kirkman (Professor of Mathematics at Wake Forest University), of the WINART network, says the group worked closely to build a supportive community.
“I distinctly remember first meeting Georgia and Ellen Kirkman at a conference at MSRI when I was a third-year graduate student,” recalls Walton. “Seeing them gave me hope that I could make it in our research field and could even be happy! Georgia was a clear inspiration early in my career, she was a pioneer, and she will be missed.”
Walton notes that Benkart’s career continued to be highly active even after retirement. Of her more than 130 published research papers, at least 45 appeared after 2007. Benkart served as president of the Association for Women in Mathematics (2009-2011), on the U.S. National Committee for Mathematics of the National Academies (2013-2020), on the Board of Trustees of the Mathematical Sciences Research Institute (2011-2022), and as associate secretary for the American Mathematical Society (2010-2022), as well as fulfilling many other service roles in the mathematics community. Among her many inspiring lectures, Georgia Benkart delivered the Noether Lecture at the International Congress of Mathematicians in 2014.
Georgia is survived by her sister Paula Benkart.
Collected Georgia Benkart Remembrances