Lauren Kiyomi Williams (born 1978) is an American mathematician known for her work on cluster algebras,

tropical geometry In mathematics, tropical geometry is the study of polynomials and their geometric properties when addition is replaced with minimization and multiplication is replaced with ordinary addition: : x\oplus y=\min\, : x\otimes y=x+y. So for exampl ...

algebraic combinatorics Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algeb ...

, amplituhedra, and the positive

Grassmannian In mathematics, the Grassmannian \mathbf_k(V) (named in honour of Hermann Grassmann) is a differentiable manifold that parameterizes the set of all k-dimension (vector space), dimensional linear subspaces of an n-dimensional vector space V over a ...

. She is Dwight Parker Robinson Professor of Mathematics at

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

Education

Williams's father is an engineer; her mother is third-generation

Japanese American are Americans of Japanese ancestry. Japanese Americans were among the three largest Asian Americans, Asian American ethnic communities during the 20th century; but, according to the 2000 United States census, 2000 census, they have declined in ...

. She grew up in Los Angeles, where her interest in mathematics was sparked by winning a fourth-grade mathematics contest. She was the

valedictorian Valedictorian is an academic title for the class rank, highest-performing student of a graduation, graduating class of an academic institution in the United States. The valedictorian is generally determined by an academic institution's grade poin ...

Palos Verdes Peninsula High School Palos Verdes Peninsula High School is a public high school in Rolling Hills Estates, Los Angeles County, California, United States, in the Los Angeles metropolitan area. As of 2023, it is a top-ranked school in the Los Angeles, CA Metro Area (#1 ...

in 1996, and while there participated in summer research at the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

with Satomi Okazaki, a student of her eventual advisor, Richard P. Stanley. She graduated

magna cum laude Latin honors are a system of Latin phrases used in some colleges and universities to indicate the level of distinction with which an academic degree has been earned. The system is primarily used in the United States. It is also used in some Sout ...

from

in 2000 with a A.B. in mathematics, and received her PhD in 2005 at the

under the supervision of Stanley. Her dissertation was titled ''Combinatorial Aspects of Total Positivity.''

Work

After postdoctoral positions at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

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. Starting in the fall of 2018, she rejoined the Harvard mathematics department as a full professor, making her the second ever tenured female math professor at Harvard. The first, Sophie Morel, left Harvard in 2012. Along with colleagues O. Mandelshtam (her former student, now an assistant professor at

University of Waterloo The University of Waterloo (UWaterloo, UW, or Waterloo) is a Public university, public research university located in Waterloo, Ontario, Canada. The main campus is on of land adjacent to uptown Waterloo and Waterloo Park. The university also op ...

) and S. 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

fellow A fellow is a title and form of address for distinguished, learned, or skilled individuals in academia, medicine, research, and industry. The exact meaning of the term differs in each field. In learned society, learned or professional society, p ...

s of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

. She is the 2016 winner of the

Association for Women in Mathematics The Association for Women in Mathematics (AWM) is a professional society whose mission is to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity for and the equal treatment o ...

and

Microsoft Microsoft Corporation is an American multinational corporation and technology company, technology conglomerate headquartered in Redmond, Washington. Founded in 1975, the company became influential in the History of personal computers#The ear ...

Research Prize in Algebra and Number Theory. In 2022 she was awarded a

Guggenheim Fellowship Guggenheim Fellowships are Grant (money), grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation, endowed by the late Simon Guggenheim, Simon and Olga Hirsh Guggenheim. These awards are bestowed upon indiv ...

Selected publications

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References

External links

Home page
* {{DEFAULTSORT:Williams, Lauren Living people Date of birth missing (living people) Year of birth missing (living people) 21st-century American mathematicians 21st-century American women mathematicians American academics of Japanese descent Combinatorialists Fellows of the American Mathematical Society Harvard College alumni Massachusetts Institute of Technology School of Science alumni University of California, Berkeley faculty Harvard University Department of Mathematics faculty