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". 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. In 2012 she became a fellow of the American Mathematical Society. In 2016 she became a fellow of the
American Academy of Arts and Sciences. In 2019, she was elected to the
National Academy of Sciences. She was named a 2021
Simons Fellows in Mathematics. 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." Kra was elected president of the
American Mathematical Society in 2021 and she served as president from February 2023 to January 2025. ==Family relations==