Lauren Kiyomi Williams

Lauren Kiyomi Williams (born 1978) is an American mathematician known for her work on cluster algebras, tropical geometry, algebraic combinatorics, amplituhedra, and the positive Grassmannian. She was awarded a MacArthur Fellowship in 2025.

Education Williams's father is an engineer; her mother is third-generation Japanese American. She grew up in Los Angeles, where she was born. Her interest in mathematics was sparked by winning a fourth-grade mathematics contest. She graduated as valedictorian of Palos Verdes Peninsula High School in 1996. where she conducted research with Satomi Okazaki, a student of her eventual Ph.D. advisor Richard P. Stanley. Her dissertation was titled Combinatorial aspects of total positivity.

Work After postdoctoral positions at the University of California, Berkeley and Harvard, Williams rejoined the Berkeley mathematics department as an assistant professor in 2009, and was promoted to associate professor in 2013 and then full professor in 2016.

Along with colleagues Olya Mandelshtam (her former student, now an assistant professor at the University of Waterloo) and Sylvie Corteel, in 2018 Williams developed a new characterization of both symmetric and nonsymmetric Macdonald polynomials using the combinatorial exclusion process.

Awards In 2012, she became one of the inaugural fellows of the American Mathematical Society. She is the 2016 winner of the Association for Women in Mathematics and Microsoft Research Prize in Algebra and Number Theory. In 2022 she was awarded a Guggenheim Fellowship. In 2025 she was awarded a MacArthur Fellowship.

Selected publications