Lauren K. Williams
Department of Mathematics, Faculty of Arts and Sciences
Seaver Professor, Radcliffe Institute for Advanced Study
Lauren K. Williams' research is in algebraic combinatorics; more specifically, she uses algebraic tools to study discrete structures in mathematics. Some of her best-known work includes combinatorial formulas for the stationary distribution of the asymmetric simple exclusion process (a model for traffic flow and translation in protein synthesis), joint with Sylvie Corteel; structural results for soliton solutions to the KP equation (often cited as a model for shallow water waves), joint with Yuji Kodama; positivity for cluster algebras from surfaces, joint with Gregg Musiker and Ralf Schiffler; a proof of the realizability of positively oriented matroids, joint with Federico Ardila and Felipe Rincon; and a polytopal manifestation of mirror symmetry for Grassmannians, joint with Konstanze Rietsch.
Williams received her BA in mathematics from Harvard College in 2000, and in 2005, after a year at the University of Cambridge doing Part III of the Mathematical Tripos, she obtained her PhD from the Massachusetts Institute of Technology under the supervision of Richard Stanley. Subsequently, she was an NSF postdoctoral fellow at the University of California, Berkeley, a Benjamin Peirce Fellow at Harvard, and a faculty member in the Department of Mathematics at UC Berkeley from 2009 to 2018, where she obtained tenure in 2013 and was promoted to full professor in 2016. She is the recipient of a Sloan Research Fellowship, an NSF CAREER award, the AWM-Microsoft Research Prize in Algebra and Number Theory, a Rose Hills Innovator Program award, a Simons Fellowship, a Distinguished Teaching & Service Award from the Mathematics Undergraduate Student Association at Berkeley, and the 2018 Hardy Lectureship from the London Mathematical Society.
Staircase tableaux, the asymmetric exclusion process, and Askey-Wilson polynomials (with Sylvie Corteel), Proceedings of the National Academy of Sciences, March 26, 2010.
Positivity for cluster algebras from surfaces (with Gregg Musiker and Ralf Schiffler), Advances in Mathematics, Volume 227, Issue 6, August 2011, 2241--2308.
KP solitons, total positivity, and cluster algebras (with Yuji Kodama), Proceedings of the National Academy of Sciences, May 11, 2011.
KP solitons and total positivity on the Grassmannian (with Yuji Kodama), Inventiones Mathematicae, Volume 198, Issue 3, December 2014.
Positively oriented matroids and realizable (with Federico Ardila and Felipe Rincon), Journal of the European Mathematical Society, 19 (2017), 815--833.