Celebratio Mathematica

Georgia Benkart

Georgia Benkart: An important mathematician
and beloved mentor

Department of Mathematics,
University of Wisconsin-Madison

In this Chapter:

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.”

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.

[Ed­it­or’s note: A se­lec­tion of re­mem­brances of Geor­gia Ben­k­art which ori­gin­ally ap­peared on the Uni­versity of Wis­con­sin’s me­mori­al page are re­pub­lished here with the au­thors’ per­mis­sion.]