Georgia Benkart

Benkart received her BS degree summa cum laude from the Ohio State University{{cite web|title=Georgia Benkart|url=https://math.osu.edu/advisory-board/georgia-benkart|website=Ohio State University Department of Mathematics|access-date=5 May 2022|archive-date=May 25, 2022|archive-url=https://web.archive.org/web/20220525095524/https://math.osu.edu/advisory-board/georgia-benkart|url-status=dead}} in 1970 and an MPhil in mathematics from Yale University in 1973. She completed her doctoral work at Yale under Nathan Jacobson and wrote a dissertation entitled Inner Ideals and the Structure of Lie Algebras. She was awarded a PhD in mathematics from the Yale University in 1974.{{cite web | title=Georgia Benkart | website=The Mathematics Genealogy Project | url=https://www.mathgenealogy.org/id.php?id=7979 | ref={{sfnref | The Mathematics Genealogy Project}} | access-date=April 30, 2022}}

Upon completing her doctoral degree, Benkart began her long career at the University of Wisconsin–Madison, first as a MacDuffee Instructor and eventually as a E. B. Van Vleck Professor of Mathematics until she retired from teaching in 2006.{{cite web|title=A Brief History of Women Mathematicians at Wisconsin |url=https://www.math.wisc.edu/history_women_mathematicians |archive-url=https://web.archive.org/web/20140529151009/https://www.math.wisc.edu/history_women_mathematicians |url-status=dead |archive-date=May 29, 2014 |publisher=University of Wisconsin Math Department |access-date=May 21, 2014 }}

She held visiting positions at the Mathematical Sciences Research Institute in Berkeley, California, the Institute for Advanced Study in Princeton, New Jersey, the Aspen Center for Physics, and the University of Virginia.{{cite web|title=Personal Profile of Dr. Georgia M. Benkart|url=https://www.msri.org/people/2676|website=Mathematical Sciences Research Institute|access-date=5 May 2022}} During her career, Benkart delivered over 350 invited talks including 3 plenary lectures at the Joint Mathematics Meetings and the Emmy Noether Lecture at the International Congress of Mathematicians in Seoul, South Korea in 2014.

Benkart was born on December 30, 1947, in Youngstown, Ohio, to George Benkart II and Florence K. Benkart. Her father served in the Army Corps of Engineers and her mother was a teacher in Youngstown's "ethnically rich south side."

Benkart died on April 29, 2022, aged 74, from undisclosed causes in Madison, Wisconsin. Her survivors included her sister, Paula Kaye Benkart.{{cite web|title=Georgia Bankart, Youngstown, Ohio|url=https://www.wkbn.com/my-valley-tributes/fox-funeral-home/georgia-bankart-youngstown-ohio/|website=MyValleyTributes|date=May 4, 2022|access-date=May 5, 2022}}

Benkart made a contribution to the classification of simple modular Lie algebras. Her work with J. Marshall Osborn on toroidal rank-one Lie algebras{{cite journal|last=Benkart|first=Georgia|author2=J. Marshall Osborn |title=Toral rank one Lie algebras|journal=Journal of Algebra|date=1988|volume=115|issue=1|pages=238–250|doi=10.1016/0021-8693(88)90293-1|doi-access=free}} became one of the building blocks of the classification. The complete description of Hamiltonian Lie Algebras (with Gregory, Osborn, Strade, Wilson) can stand alone, and also has applications in the theory of pro-p groups.

In 2009, she published, jointly with Thomas Gregory and Alexander Premet, the first complete proof of the recognition theorem for graded Lie algebras in characteristics at least 5.Review of The recognition theorem for graded Lie algebras in prime characteristic by Murray R. Bremner (2009); {{MR|2488391}}

In the early 1990s, Benkart and Efim Zelmanov started to work on classification of root-graded Lie algebras and intersection matrix algebras. The latter were introduced by Peter Slodowy in his work on singularities. Berman and Moody recognized that these algebras (generalizations of affine Kac–Moody algebras) are universal root graded Lie algebras and classified them for simply laced root systems. Benkart and Zelmanov tackled the remaining cases involving the Freudenthal magic square and extended this square to exceptional Lie superalgebras.

Later Benkart extended these results in two directions. In a series of papers with Alberto Elduque she developed the theory of root graded Lie superalgebras.{{cite journal | last1=Martínez | first1=Consuelo | last2=Zelmanov | first2=Efim I. | title=Lie superalgebras graded by P ( n ) and Q ( n ) | journal=Proceedings of the National Academy of Sciences | volume=100 | issue=14 | date=2003-06-27 | issn=0027-8424 | doi=10.1073/pnas.0932706100 | pages=8130–8137| pmid=12832611 | pmc=166194 | bibcode=2003PNAS..100.8130M | doi-access=free }} In a second series of works with Bruce Allison, Arturo Pianzola, Erhard Neher, et al. she determined the universal central covers of these algebras.{{cite journal| last1=Benkart| first1=Georgia| last2=Neher| first2=Erhard| title=The centroid of extended affine and root graded Lie algebras| journal=J. Pure Appl. Algebra|volume=205|issue=1|date = 2006| pages=117–145| doi=10.1016/j.jpaa.2005.06.007|mr=2193194| s2cid=14256793| doi-access=free| arxiv=math/0502561}}

One of the pillars of the representation theory of quantum groups (and applications to combinatorics) is Masaki Kashiwara's theory of crystal bases. These are highly invariant bases which are well suited for decompositions of tensor products. In a paper with Seok-Jin Kang and Kashiwara, Benkart extended the theory of crystal bases to quantum superalgebras.{{cite journal |last1=Benkart |first1=Georgia |last2=Kang |first2=Seok-Jin |last3=Kashiwara |first3=Masaki |title=Crystal bases for the quantum superalgebra U_q(𝔤𝔩(m,n)). |journal=J. Amer. Math. Soc. |date=2000 |volume=13 |issue=2 |pages=295–331 |doi=10.1090/S0894-0347-00-00321-0 |mr=1694051|doi-access=free }}

Benkart's work on noncommutative algebras related to algebraic combinatorics became a basic tool in the construction of tensor categories.

Benkart served on several editorial boards including the boards of the American Mathematical Society for Surveys and Monographs and Abstracts,{{cite web|title=Mathematical Surveys and Monographs Editorial Committee Past Members|url=https://www.ams.org/about-us/governance/committees/mathsurv-past.html |publisher=American Mathematical Society|access-date=May 6, 2022}} Communications in Algebra,{{cite journal |title=Editorial board |journal=Communications in Algebra |date=1 January 1987 |volume=15 |issue=6 |page=ebi |doi=10.1080/00927878708823457 |url=https://www.tandfonline.com/doi/abs/10.1080/00927878708823457 |access-date=6 May 2022 |issn=0092-7872}} and the Journal of Algebra.{{cite web|title=Georgia Benkart|url=https://www.maa.org/georgia-benkart|website=Mathematical Association of America|access-date=May 6, 2022}} She served as the associate secretary of the American Mathematical Society for the Central Section from 2010 to 2020,{{cite web |title=American Mathematical Society Council {{!}} February 1, 2017 - January 31, 2018 |url=https://www.ams.org/about-us/governance/council/member-council |access-date=6 May 2022 |archive-url=https://web.archive.org/web/20170204085756/https://www.ams.org/about-us/governance/council/member-council |archive-date= February 4, 2017 |format=web.archive.org |quote=Professor Georgia Benkart Associate Secretary (Central Section) Term: February 1, 2010 - January 31, 2020 University of Wisconsin, Madison}} and was a member of the governing council in 1995 and from 2010 to 2021.{{cite web|title=Council Past Members|url=https://www.ams.org/about-us/governance/committees/council-past.html |publisher=American Mathematical Society|access-date=May 6, 2022}} Benkart was active in the Association for Women in Mathematics (AWM) over many years, served as chair of the membership portfolio and the nominating committee, and helped plan the first AWM Research Symposium, which was also a celebration of the 40th anniversary of AWM.{{cite web|title=Committees|publisher=Association for Women in Mathematics|url=https://awm-math.org/about/committees/|access-date=May 6, 2022}}

Benkart received a Woodrow Wilson Fellowship from the Woodrow Wilson National Fellowship Foundation. Her work at Wisconsin was recognized by a Romnes Fellowship in 1985, a Distinguished Teaching Award in 1987, and a WARF Mid-Career Faculty Research Award in 1996.{{cite web|title=University of Wisconsin Honors and Awards|url=http://www.math.wisc.edu/oldhome/news/2001/awards.htm|publisher=University of Wisconsin|accessdate=May 23, 2014|archive-date=January 21, 2020|archive-url=https://web.archive.org/web/20200121091755/https://www.math.wisc.edu/oldhome/news/2001/awards.htm|url-status=dead}} In 2008 the University of California Lie Groups and Lie Algebras meeting was held in Benkart's honor. Her talks and lectures include two invited lectures at the Joint Mathematics Meetings{{cite web|title=Joint Mathematics Meeting AMS-MAA Invited Address|url=http://jointmathematicsmeetings.org/meetings/national/jmm/1889_program_wednesday.html#1889:BENKART|publisher=American Mathematical Society|accessdate=May 23, 2014}} and a plenary lecture at a meeting of the Canadian Mathematical Society.{{cite web|title=2001 CMS Summer Meeting|url=https://cms.math.ca/Events/summer01/photos/CMSindex.html#plenary|website=Photos from the 2001 CMS Summer Meeting|publisher=Canadian Mathematical Society|accessdate=June 10, 2014}}

In 2000–2002 Benkart was named a Polya Lecturer{{cite web|title=Pólya Lectures|url=http://www.maa.org/programs/maa-awards/lecture-awards/pólya-lecturers|publisher=Mathematical Association of America|accessdate=May 21, 2014}} by the Mathematical Association of America.

She was elected a Fellow of the American Mathematical Society (AMS){{cite web|title=List of Fellows of the American Mathematical Society|url=https://www.ams.org/profession/fellows-list|publisher=American Mathematical Society|accessdate=May 21, 2014}} in the inaugural class of 2013.

She was elected and served as president of the Association for Women in Mathematics from 2009 to 2011.{{cite journal|title=President's Report|journal=AWM Newsletter|date=March–April 2009|volume=39|issue=2|pages=1–5|access-date=27 May 2014|url=http://www.drivehq.com/file/df.aspx/isGallarytrue/shareID8755087/fileID929339010?1=1}} In 2014 she was selected to deliver the AWM-AMS Noether Lecture.{{cite web|title=List of Noether Lecturers|url=https://awm-math.org/awards/noether-lectures/|accessdate=January 26, 2019}} The title of her talk was Walking on Graphs the Representation Theory Way.{{cite web|title=Noether Lecture Profile|url=https://awm-math.org/awards/noether-lectures/noether-lectures-2014/|publisher=Association for Women in Mathematics|accessdate=January 26, 2019}}

In 2014 at the International Congress of Mathematicians held in Seoul, she delivered the ICM Emmy Noether Lecture.{{cite web|title=ICM Emmy Noether Lecture |url=http://www.icm2014.org/en/program/scientific/speciallectures |publisher=the organizing committee of Seoul ICM 2014 |accessdate=October 2, 2014 |url-status=dead |archiveurl=https://web.archive.org/web/20141006121521/http://www.icm2014.org/en/program/scientific/speciallectures |archivedate=October 6, 2014 }}

She was selected as a fellow of the Association for Women in Mathematics in the inaugural 2018 class.{{cite web|title=2018 Inaugural Class of AWM Fellows|url=https://awm-math.org/awards/awm-fellows/2018-awm-fellows/|publisher=Association for Women in Mathematics|accessdate=November 23, 2020}}

In 2022, a tribute to her contributions to her field, "Gems from the Work of Georgia Benkart", appeared in the Notices of the American Mathematical Society.{{cite journal|title=Gems from the Work of Georgia Benkart|journal=Notices of the American Mathematical Society|date=March 2022|volume=69|issue=3|pages=375–384|accessdate=April 30, 2022|url=https://www.ams.org/journals/notices/202203/rnoti-p375.pdf}}

The American Mathematical Society{{cite web|title=Remembering Georgia Benkart (1947 - 2022)|website=American Mathematical Society|url=https://www.ams.org/news?news_id=7023|access-date=4 May 2022}} and the University of Wisconsin–Madison mathematics department{{cite web|title=Georgia Benkart Remembrances|website=University of Wisconsin – Madison Mathematics|url=https://math.wisc.edu/georgia-benkart-rememberances/|access-date=4 May 2022}} posted remembrances of Benkart.

• with Daniel Britten, Frank Lemire: {{cite book|title=Stability in Modules for Classical Lie Algebras: A Constructive Approach|series=Memoirs of the American Mathematical Society|volume=85|location=Providence, R.I.|publisher=American Mathematical Society|year=1990|url=https://books.google.com/books?id=d0F-R0eZSqkC|mr=1010997|isbn=9780821861530}}
• with Seok-Jin Kang, Masaki Kashiwara: {{cite journal |last1=Benkart |first1=Georgia |last2=Kang |first2=Seok-Jin |last3=Kashiwara |first3=Masaki |title=Crystal bases for the quantum superalgebra U_q(𝔤𝔩(m,n)). |journal=J. Amer. Math. Soc. |date=2000 |volume=13 |issue=2 |pages=295–331 |doi=10.1090/S0894-0347-00-00321-0 |mr=1694051|doi-access=free }}
• with Bruce Allison, Yun Gao: {{cite book|title=Lie algebras graded by the root systems BC_r, r ≥ 2|series=Memoirs of the American Mathematical Society|volume=158|publisher=American Mathematical Society|year=2002|url=https://books.google.com/books?id=Wb48-RBngkYC|mr=1902499|isbn=9780821864739}}
• with Thomas Gregory, Alexander Premet: {{cite book|title=The recognition theorem for graded Lie algebras in prime characteristic|series=Memoirs of the American Mathematical Society|volume=197|publisher=American Mathematical Society|year=2009| url=https://books.google.com/books?id=jxS9AwAAQBAJ |isbn= 9780821842263|arxiv= math/0508373 |mr=2488391 |last1=Benkart |first1=Georgia |last2=Gregory |first2=Thomas |last3=Premet |first3=Alexander }}

{{reflist|30em}}

• Georgia Benkart's [https://www.ams.org/mathscinet/MRAuthorID/34650 Author Profile Page] on MathSciNet
• {{MathGenealogy | ID=7979 }}
• {{cite journal|title=Remembering Georgia Benkart|journal=Notices of the American Mathematical Society|date=March 2023|volume=70|issue=3|pages=420–433|url=https://www.ams.org/notices/202303/rnoti-p420.pdf|doi=10.1090/noti2653|doi-access=free |last1=Adem |first1=Alejandro |last2=Halverson |first2=Tom |last3=Ram |first3=Arun |last4=Zelmanov |first4=Efim |last5=Sundaram |first5=Sheila |last6=Pianzola |first6=Arturo |last7=Charney |first7=Ruth |last8=Kirkman |first8=Ellen |last9=Farnsteiner |first9=Rolf |last10=Elduque |first10=Alberto |last11=Christodoulopoulou |first11=Konstantina |last12=Witherspoon |first12=Sarah |last13=Zelmanov |first13=Efim |last14=Orellana |first14=Rosa |last15=Barcelo |first15=Hélène |last16=Nakano |first16=Daniel }}

{{AWM Presidents}}

{{authority control}}

{{DEFAULTSORT:Benkart, Georgia}}

Category:1947 births

Category:2022 deaths

Category:Deaths from lung cancer in Wisconsin

Category:People from Youngstown, Ohio

Category:20th-century American mathematicians

Category:21st-century American mathematicians

Category:20th-century American women mathematicians

Category:21st-century American women mathematicians

Category:Yale Graduate School of Arts and Sciences alumni

Category:University of Wisconsin–Madison faculty

Category:Ohio State University alumni

Category:Fellows of the American Mathematical Society

Category:Mathematicians from Ohio

Category:Fellows of the Association for Women in Mathematics

Category:Aspen Center for Physics people