Bryna Kra
Bryna Rebekah Kra

1966 (age 56–57)
Alma materStanford University, Harvard University
Known forErgodic theory
AwardsLevi L. Conant Prize (2010)
Scientific career
InstitutionsNorthwestern University
University of Michigan
ThesisCommutative groups of diffeomorphisms of the circle (1995)
Doctoral advisorYitzhak Katznelson

Bryna Rebekah Kra (born 1966) is an American mathematician and Sarah Rebecca Roland Professor at Northwestern University who is on the board of trustees of the American Mathematical Society and was elected the president of American Mathematical Society in 2021. As a member of American Academy of Arts and Sciences and National Academy of Sciences, Kra has made significant contributions to the structure theory of characteristic factors for multiple ergodic averages. Her academic work centered on dynamical systems[1] and ergodic theory, and uses dynamical methods to address problems in number theory and combinatorics.[2]

Education and career

Kra was born in 1966 in Boston.[3] She graduated with a bachelor's degree from Harvard University in 1988, and obtained her Ph.D. from Stanford University in 1995 under the guidance of Yitzhak Katznelson.[4] She held postdoctoral positions at the Hebrew University in Jerusalem, the University of Michigan, the IHÉS and the Ohio State University before joining the mathematics faculty at Pennsylvania State University as an assistant professor. Since 2004 Kra has been a professor of mathematics at Northwestern University, where she was department chair from 2009 to 2012.


With Bernard Host, Kra is the author of the book Nilpotent Structures in Ergodic Theory (Mathematical Surveys and Monographs 236, American Mathematical Society, 2018).


In 2010 Kra was awarded the Levi L. Conant Prize for her expository article "The Green–Tao theorem on arithmetic progressions in the primes: an ergodic point of view".[5][6] In 2006 she was an invited speaker at the International Congress of Mathematicians in Madrid ("From combinatorics to ergodic theory and back again"), and was named an AMS Centennial Fellow the same year.[7] In 2012 she became a fellow of the American Mathematical Society.[8] In 2016 she became a fellow of the American Academy of Arts and Sciences.[9] In 2019, she was elected to the National Academy of Sciences.[10] She was named a 2021 Simons Fellows in Mathematics.[11] Kra was elected to the 2023 class of fellows of the Association for Women in Mathematics "for her vision and work creating programs to support women in mathematics, especially GROW (Graduate Research Opportunities for Women) and AWM student chapters; for her leadership in the mathematics community, including serving on the AWM Executive Committee and serving as president of AMS; and for making advocacy for women a priority throughout her career."[12] Kra was elected president of the American Mathematical Society and assumed that position on February 1, 2023.[13]

Family relations

Kra is the daughter of mathematician Irwin Kra.[14]


  1. ^ Crowell, Rachel (November 17, 2020), "Searching Symbols for the Rules of Change: Bryna Kra searches for the patterns in sequences of numbers that explain how complicated dynamical systems evolve over time", Quanta Magazine
  2. ^ Host, Bernard; Kra, Bryna (2005), "Nonconventional ergodic averages and nilmanifolds" (PDF), Annals of Mathematics, Second Series, 161 (1): 397–488, doi:10.4007/annals.2005.161.397, MR 2150389.
  3. ^ "Bryna Kra" (PDF), Biographies of Candidates 2015, Notices of the American Mathematical Society, 62 (8): 942, September 2015
  4. ^ Bryna Kra at the Mathematics Genealogy Project
  5. ^ Kra, Bryna (2006), "The Green-Tao theorem on arithmetic progressions in the primes: an ergodic point of view", Bulletin of the American Mathematical Society, New Series, 43 (1): 3–23, doi:10.1090/S0273-0979-05-01086-4, MR 2188173
  6. ^ "2010 Conant Prize" (PDF), Notices of the American Mathematical Society, 57 (4): 515–516, April 2010.
  7. ^ Jackson, Allyn (June–July 2006), "2006–2007 AMS Centennial Fellowships Awarded" (PDF), Mathematics People, Notices of the American Mathematical Society, 53 (6): 686.
  8. ^ List of Fellows of the American Mathematical Society, retrieved 2013-07-07.
  9. ^ Newly Elected Members, American Academy of Arts and Sciences, April 2016, retrieved 2016-04-20
  10. ^ "National Academy of Sciences Elects Members and Foreign Associates; Historic Number of Women Elected to Its Membership", News from the National Academy of Sciences, April 30, 2019
  11. ^ "2021 Simons Fellows in Mathematics and Theoretical Physics Announced". Simons Foundation. 2021-02-04. Retrieved 2021-07-18.
  12. ^ "The AWM Fellows Program: 2023 Class of AWM Fellows". Association for Women in Mathematics. Retrieved 23 October 2022.
  13. ^ "Kra Takes Helm of AMS Presidency". American Mathematical Society. Retrieved 10 April 2023.
  14. ^ Irwin Kra, Math for America board, retrieved 2016-06-24.