About

Brooke Williams is an associate professor of the practice of computational journalism at Boston University College of Communication. She is an investigative reporter specializing in data journalism, with her work contributing to prestigious awards including a Pulitzer Prize for Investigative Reporting, a George Polk Award, and a Gerald Loeb Award. Williams has co-authored and built databases for front-page investigations into think tanks, foreign governments, corporations, and influence, notably contributing to The New York Times. Her investigative work at the Center for Public Integrity included the award-winning 'Windfalls of War,' an investigation into defense contracts in Iraq and Afghanistan, and she co-authored 'Harmful Error: Investigating America’s Local Prosecutors.' She has also contributed to the bestselling book 'The Buying of the President 2004.' Early in her career, Williams worked as an investigative reporter at The San Diego Union-Tribune, focusing on wildfire cleanup and city finances. She was a residential journalism fellow at the Edmond J. Safra Center for Ethics at Harvard University. Her data-driven investigations have been featured in print, online, radio, and TV outlets such as ABC World News, inewsource, and NPR. Currently, she is a contributor to The Intercept and is working on a multi-year investigation into federal prosecutors utilizing machine learning. Williams emphasizes publishing work from her courses, including features, hard news, investigations, and data projects, and is dedicated to mentoring students interested in investigative and data-driven journalism.

Research topics

• Physics
• Geometry
• Mathematics
• Mathematical physics
• Pure mathematics
• Quantum mechanics

Selected publications

• On the renormalization and quantization of topological–holomorphic field theories

  Advances in Mathematics · 2026-04-23

  preprintOpen accessSenior authorCorresponding
  PublisherOA PDFDOI

• Holomorphic field theories and higher algebra

  Bulletin of the London Mathematical Society · 2025-07-21

  articleOpen accessSenior author

  Abstract Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogs of the rich interplay between Riemann surfaces, Virasoro and Kac‐Moody Lie algebras, and conformal blocks. We introduce a panoply of examples from physics — field theories that are holomorphic in nature, such as holomorphic Chern‐Simons theory — and interpret them as (derived) moduli spaces in complex geometry; no comfort with physics is presumed. We then describe frameworks for quantizing such moduli spaces, offering a systematic generalization of vertex algebras and conformal blocks via factorization algebras, and we explain how holomorphic field theories generate examples of these higher algebraic structures. We finish by describing how the conjecture of Seiberg duality predicts a surprising relationship between holomorphic gauge theories on algebraic surfaces and how it suggests analogs of the Hori–Tong dualities already studied by algebraic geometers.

  PublisherDOI

• Higgs and Coulomb branches from superconformal raviolo vertex algebras

  Advances in Mathematics · 2025-10-09 · 1 citations

  articleSenior authorCorresponding
  PublisherDOI

• Raviolo vertex algebras

  Selecta Mathematica · 2025-04-28 · 3 citations

  articleSenior author
  PublisherDOI

• Unravelling the Holomorphic Twist II: Anomalies and Extended Supersymmetry

  ArXiv.org · 2025-09-20

  preprintOpen access

  Twists of four-dimensional supersymmetric quantum field theories (SQFTs) isolate protected sectors with rich algebraic structures. We develop a unified framework for analyzing symmetries and anomalies in four-dimensional holomorphically twisted SQFTs, combiningcomplex-geometric and algebraic perspectives. This approach clarifies the connections between existing formulations in the literature and resolves several open questions left unanswered in the first installment of this series. We place particular emphasis on theories with extended supersymmetry, where the holomorphic twist gives rise to enhanced algebraic and geometric structures. We explain how these features emerge and govern the organization of the twisted theory. Furthermore, we demonstrate how a superconformal deformation of the twisted theory naturally leads to the associated vertex operator algebra, clarifying how the higher algebraic structures of the holomorphically twisted theory give rise to vertex algebras structures.

  PublisherOA PDFDOI

• Twisting pure spinor superfields, with applications to supergravity

  Pure and Applied Mathematics Quarterly · 2024-01-01 · 16 citations

  articleSenior author

  We study twists of supergravity theories and supersymmetric field theories, using a version of the pure spinor superfield formalism. Our results show that, just as the component fields of supersymmetric multiplets are the vector bundles associated to the equivariant Koszul homology of the variety of square-zero elements in the supersymmetry algebra, the component fields of the holomorphic twists of the corresponding multiplets are the holomorphic vector bundles associated to the equivariant Koszul homology of square-zero elements in the twisted supersymmetry algebra. The BRST or BV differentials of the free multiplet are induced by the brackets of the corresponding super Lie algebra in each case. We make this precise in a variety of examples; applications include rigorous computations of the minimal twists of eleven-dimensional and type IIB supergravity, in the free perturbative limit. The latter result proves a conjecture by Costello and Li, relating the IIB multiplet directly to a presymplectic BV version of minimal BCOV theory.

  PublisherDOI

• Local superconformal algebras

  arXiv (Cornell University) · 2024-10-10

  preprintOpen accessSenior author

  Given a supermanifold equipped with an odd distribution of maximal dimension and constant symbol, we construct the formal moduli problem of deformations of the distribution. This moduli problem is described by a local super dg Lie algebra that provides both a resolution of the structure-preserving vector fields on superspace and a derived enhancement of superconformal symmetry. Applying our construction in standard physical examples returns the conformal supergravity multiplet in every known example, in any dimension and with any amount of supersymmetry$\unicode{x2014}$whether or not a superconformal algebra exists. We discuss new examples related to twisted supergravity, higher Virasoro algebras, and exceptional super Lie algebras. The compatibility of our techniques with twisting also leads to a computation of every twist of the stress tensor multiplet of a superconformal theory, including universal operator product expansions. Our approach uses a derived model for the space of functions constant along the distribution, which is applicable even when the distribution is non-involutive; we construct other natural multiplets, such as Kähler differentials, that appear naturally through this lens on superspace geometry.

  PublisherOA PDFDOI

• Semi-chiral operators in 4d $$ \mathcal{N} $$ = 1 gauge theories

  Journal of High Energy Physics · 2024-05-22 · 11 citations

  articleOpen access

  A bstract We discuss the properties of quarter-BPS local operators in four-dimensional $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 1 supersymmetric Yang-Mills theory using the formalism of holomorphic twists. We study loop corrections both to the space of local operators and to algebraic operations which endow the twisted theory with an infinite symmetry algebra. We classify all single-trace quarter-BPS operators in the planar approximation for SU( N ) gauge theory and propose a holographic dual description for the twisted theory. We classify perturbative quarter-BPS operators in SU(2) and SU(3) gauge theories with sufficiently small quantum numbers and discuss possible non-perturbative corrections to the answer. We set up analogous calculations for some theories with matter.

  PublisherOA PDFDOI

• A holomorphic approach to fivebranes

  Proceedings of symposia in pure mathematics · 2024-05-08

  other1st authorCorresponding

  We present an approach to studying the algebra of local operators on a stack of finitely many fivebranes in M theory at the level of the holomorphic twist. Our approach is through the lens of twisted holography and utilizes a description of the minimal twist of eleven-dimensional supergravity.

  PublisherDOI

• Higher Deformation Quantization for Kapustin–Witten Theories

  Annales Henri Poincaré · 2024-02-16 · 3 citations

  articleSenior author
  PublisherDOI

Frequent coauthors

• B.F. Mason

  Institute for Microstructural Sciences

  41 shared

• Owen Gwilliam

  18 shared

• Justin Kulp

  Perimeter Institute

  17 shared

• Matthew Yu

  University of Oxford

  17 shared

• Kasia Budzik

  Perimeter Institute

  17 shared

• Davide Gaiotto

  17 shared

• Jingxiang Wu

  University of Oxford

  17 shared

• Ingmar Saberi

  Ludwig-Maximilians-Universität München

  13 shared

Awards & honors

• Pulitzer Prize for Investigative Reporting
• George Polk Award
• Gerald Loeb Award