AWM Microsoft Research Prize in Algebra and Number Theory 2016


The 2016 AWM Microsoft Research Prize in Algebra and Number Theory is presented to Professor Lauren Williams, in recognition of her exceptional research in algebraic combinatorics.

Professor Williams received her doctorate in 2005 from the Massachusetts Institute of Technology. After appointments at MSRI, Berkeley, and Harvard, she is currently an Associate Professor of Mathematics at the University of California, Berkeley.

Professor Williams is a powerful and broad combinatorialist, whose scientific reach extends into representation theory, algebraic geometry and physics. Her early work on the totally nonnegative Grassmannian is a beautiful and fundamental contribution to our understanding of the combinatorics— and later (with Rietsch), the topology— of this space which has important connections to Lusztig’s work on canonical bases in representation theory. Professor Williams is also a leader in the exciting new subject of cluster algebras. She (with Musiker and Schiffler) proved an important special case of the famous Laurent positivity conjecture (now a theorem); their proof is a technical tour de force, which unlike some other approaches, yields a transparent combinatorial rule for the Laurent polynomials in question. Her paper with Ardila and Rincon, in which an old conjecture about realizability of positively oriented matroids is finally established, has been hailed by experts as the “climax of the study of positroids in the past decade.” Most recently, her work with Kodama brings her expertise into the entirely new direction of soliton solutions of the KP equation and modeling shallow water waves.

Beyond her outstanding scientific achievements, Professor Williams has assumed many leadership roles in the mathematical community and is a dedicated PhD and post-doctoral adviser.

We congratulate Professor Williams for her well-deserved AWM Microsoft Research Prize!

Response from Lauren Williams

I am deeply honored to be receiving this award, and would like to thank the AWM and Microsoft for their generosity in establishing it, as well as my mentors and colleagues who nominated me for the award. I am profoundly grateful to have had numerous wonderful mentors, from childhood up until now, but I would like to mention in particular my thesis advisor Richard Stanley and my colleague Bernd Sturmfels, as well as Sara Billey and Sergey Fomin. Mathematics is rarely a solitary endeavor these days, and I am happy to acknowledge my many collaborators (now friends), including Sylvie Corteel, Yuji Kodama, Konstanze Rietsch, Federico Ardila and Felipe Rincon, and Gregg Musiker and Ralf Schiffler.
Finally I would like to thank the math department and my colleagues at UC Berkeley, for providing me with such a supportive and welcoming mathematical “home.”

I don’t think that anyone completely understands why women are still a minority among mathematicians. But ever since the Association for Women in Mathematics was established, this organization has played an important role in bringing together the community of women mathematicians, and reminding us all that there are many women mathematicians out there doing excellent work. The various activities, meetings, and lectures that the AWM has sponsored have provided a lot of inspiration and support to me personally, as I know they have done for countless others. Thanks again!