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Overview

Lauren Williams is affiliated with Harvard University in the United States and conducts research primarily in the field of Mathematics. Their research spans a variety of subfields including Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics, Statistics and Probability, and Statistical and Nonlinear Physics.

The main topics of Lauren Williams' work encompass advanced combinatorial mathematics, algebraic structures and combinatorial models, random matrices and their applications, stochastic processes and statistical mechanics, nonlinear waves and solitons, advanced topics in algebra, and coding theory and cryptography.

Lauren Williams has published extensively, with 62 publications in mathematics overall. They have contributed to several notable publication venues, with the largest number of papers appearing in arXiv (Cornell University), where they have 16 publications. Other frequent venues include Oberwolfach Reports with 3 publications, International Mathematics Research Notices with 2, American Journal of Mathematics, and Advances in Mathematics with 1 publication each.

Some of the recent papers authored or coauthored by Lauren Williams include:

  • The Positive Tropical Grassmannian, the Hypersimplex, and the m= 2 Amplituhedron, 2023, International Mathematics Research Notices
  • From multiline queues to Macdonald polynomials via the exclusion process, 2022, American Journal of Mathematics
  • Higher secondary polytopes and regular plabic graphs, 2022, Advances in Mathematics
  • The positive tropical Grassmannian, the hypersimplex, and the m=2 amplituhedron, 2020, arXiv (Cornell University)
  • The =2 amplituhedron and the hypersimplex: Signs, clusters, tilings, Eulerian numbers, 2023, Communications of the American Mathematical Society

Lauren Williams frequently collaborates with several coauthors, including Matteo Parisi, Melissa Sherman-Bennett, Ran J. Tessler, Chaim Even-Zohar, and Tsviqa Lakrec. These collaborations have contributed to various papers and research projects across the scientist's areas of study.

Best Publications

  • Faces of Generalized Permutohedra

    Alexander Postnikov;Victor Reiner;Lauren Williams

  • Positivity for cluster algebras from surfaces

    Gregg Musiker;Ralf Schiffler;Lauren Williams

  • The Tropical Totally Positive Grassmannian

    David Speyer;Lauren Williams

  • KP solitons and total positivity for the Grassmannian

    Yuji Kodama;Lauren Williams

  • Tableaux combinatorics for the asymmetric exclusion process

    Sylvie Corteel;Lauren K. Williams

  • Enumeration of totally positive Grassmann cells

    Lauren K. Williams

  • Bases for cluster algebras from surfaces

    Gregg Musiker;Ralf Schiffler;Lauren Williams

  • Permutation tableaux and permutation patterns

    Einar Steingrímsson;Lauren K. Williams

  • Tableaux combinatorics for the asymmetric exclusion process and Askey-Wilson polynomials

    Sylvie Corteel;Lauren K. Williams

  • Matching polytopes, toric geometry, and the totally non-negative Grassmannian

    Alexander Postnikov;David Speyer;Lauren Williams

  • Introduction to Cluster Algebras. Chapters 1-3

    Sergey Fomin;Lauren Williams;Andrei Zelevinsky

  • The Deodhar decomposition of the Grassmannian and the regularity of KP solitons

    Yuji Kodama;Lauren Williams

  • Cluster algebras: an introduction

    Lauren K. Williams

  • A Markov Chain on Permutations which Projects to the PASEP

    Sylvie Corteel;Lauren K. Williams

  • Bruhat interval polytopes

    Emmanuel Tsukerman;Lauren Williams

  • Newton–Okounkov bodies, cluster duality, and mirror symmetry for Grassmannians

    Konstanze Rietsch;Lauren Williams

  • KP solitons, total positivity, and cluster algebras

    Yuji Kodama;Lauren K. Williams

  • The $m=1$ Amplituhedron and Cyclic Hyperplane Arrangements

    Steven N Karp;Lauren K Williams

  • Matrix Formulae and Skein Relations for Cluster Algebras from Surfaces

    Gregg Musiker;Lauren Williams

  • Cluster algebras

    Bernard Leclerc;Lauren K. Williams

Frequent Co-Authors

Yuji Kodama
Yuji Kodama The Ohio State University
David E Speyer
David E Speyer University of Michigan–Ann Arbor
Wesley I. Sundquist
Wesley I. Sundquist University of Utah
Thomas Lam
Thomas Lam University of Michigan–Ann Arbor
Josep M. Mercader
Josep M. Mercader Broad Institute
Victor Reiner
Victor Reiner University of Minnesota
David Torrents
David Torrents Barcelona Supercomputing Center
Bernd Sturmfels
Bernd Sturmfels Max Planck Institute for Mathematics in the Sciences

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