Lauren K. Williams Named Among 2025 "Genius Grant" Recipients
Lauren K. Williams, von Neumann Fellow (2017) in the Schools of Mathematics and Natural Sciences, has been named a 2025 MacArthur Fellow. Often referred to as the "genius grant," MacArthur Fellowships invest in individuals demonstrating exceptional creativity and potential for future advances.
The Fellowship recognizes Williams’s influential and wide-ranging research that bridges algebraic combinatorics, geometry, and physics.
In the MacArthur Foundation citation, Williams was praised for having made "significant contributions to numerous mathematical fields, including cluster algebras, representation theory, and algebraic geometry. She has also forged cross-disciplinary collaborations to tackle long-standing and challenging problems in physics related to quantum field theory, particle physics, and wave propagation."
Delving into the specifics of her work, the citation continued: "Much of Williams’s research centers on using combinatorial approaches to understand the nature of the positive Grassmannian. A Grassmannian is a geometric space that encompasses all of the multidimensional planes of a fixed dimension. The positive Grassmannian is the portion with only positive coordinates. In early work, Williams explored how points (formed by the multidimensional planes) in the positive Grassmannian divide it into cells—basically, the puzzle pieces that make it up. She determined several characteristics of the cells, including a formula for the number of different cells in a positive Grassmannian of any dimension."
More recently, Williams has collaborated with mathematicians and particle physicists to bring the combinatorics of the positive Grassmannian to bear on scattering amplitudes—namely, the probabilities of different outcomes when fundamental particles collide. She developed mathematical proofs for the amplituhedron, a geometric object encoding particle-scattering processes discovered in 2013 by Nima Arkani-Hamed, Gopal Prasad Professor in the School of Natural Sciences, and Jaroslav Trnka.
Williams’s selection as a MacArthur Fellow highlights the curiosity-driven, cross-disciplinary spirit of the Institute’s community; during her time as a von Neumann Fellow, she benefited from the Institute's unique environment, one that brings together researchers whose ideas resonate across fields. With this honor, she joins a distinguished cohort of IAS-affiliated scholars recognized by the MacArthur Foundation, including, in recent years, E. Tendayi Achiume, Ashvin B. Chhabra and Daniela Bonafede-Chhabra Member (2024–25) in the School of Social Science, who was part of the Class of 2023 of MacArthur fellows. AMIAS Members Ruha Benjamin (2016–17) and Jennifer L. Morgan (2014–15), also in the School of Social Science, were recipients of 2024 Fellowships.
Read more on the MacArthur Foundation website.
