About

Angela Gibney is a Professor of Mathematics and a Presidential Professor of Mathematics at the University of Pennsylvania, where she also serves as the Graduate Chair in the Department of Mathematics. Her research interests include algebraic geometry and representation theory. She is part of the standing faculty at the department, contributing to both teaching and research activities. Her contact information includes her office at 3E3 DRL, with phone number 215-898-7846 and email agibney@math.upenn.edu.

Research topics

• Mathematics
• Pure mathematics
• Combinatorics
• Geometry
• Computer science

Selected publications

• Basepoint Free Cycles on M0,n from Gromov–Witten Theory

  UNC Libraries · 2026-04-17

  articleOpen access1st authorCorresponding

  Basepoint free cycles on the moduli space M0,n of stable n-pointed rational curves, defined using Gromov–Witten invariants of smooth projective homogeneous spaces are introduced and studied. Intersection formulas to find classes are given. Gromov–Witten divisors for projective space are shown equivalent to conformal blocks divisors for type A at level 1.

  PublisherDOI

• Strong Unital Property of Vertex Operator Algebras

  Scholarly Commons (University of Pennsylvania) · 2025-09-15

  otherOpen access

  This project investigates when irrational vertex operator algebras (VOAs) satisfy the strong unital property. We will focuses on two families of irrational VOAs: the orbifold Heisenberg VOA and the affine Lie algebra VOA at irrational level. Our strategy is to translate the verification of the strong unital property into a problem of solving a large system of algebraic equations derived from explicit structural data. VOAs that satisfy this property give rise to generalized Verlinde bundles, vector bundles on the moduli space of stable curves which play a central role in moduli theory and conformal field theory.

  Publisher

• Conformal Blocks on Smoothings via Mode Transition Algebras

  Communications in Mathematical Physics · 2025-05-07 · 2 citations

  articleOpen access

  Abstract Here we introduce a series of associative algebras attached to a vertex operator algebra V of CFT type, called mode transition algebras, and show they reflect both algebraic properties of V and geometric constructions on moduli of curves. Pointed and coordinatized curves, labeled by admissible V -modules, give rise to sheaves of coinvariants. We show that if the mode transition algebras admit multiplicative identities satisfying certain natural properties (called strong identity elements), these sheaves deform as wanted on families of curves with nodes. This provides new contexts in which coherent sheaves of coinvariants form vector bundles. We also show that mode transition algebras carry information about higher level Zhu algebras and generalized Verma modules. To illustrate, we explicitly describe the higher level Zhu algebras of the Heisenberg vertex operator algebra, proving a conjecture of Addabbo–Barron.

  PublisherOA PDFDOI

• Morita equivalences for Zhu's algebra

  arXiv (Cornell University) · 2024-03-18

  preprintOpen access

  Through the introduction of new ideals, and with the assistance of the $d$-th mode transition algebras $\mathfrak{A}_d$, for $d\in \mathbb{N}$, we show how Zhu's associative algebra $\mathsf{A}$, conventionally valued for tracking information about the degree $0$ part of an $\mathbb{N}$-graded module over a vertex operator algebra $V$, also contains information about components of higher degree. As an application, equivalent conditions are given for rationality of $V$, and explicit presentations for higher-level Zhu algebras are given, including for a large class of non-rational VOAs.

  PublisherOA PDFDOI

• On factorization and vector bundles of conformal blocks from vertex algebras

  Annales Scientifiques de l École Normale Supérieure · 2024-04-02 · 11 citations

  article

  Modules over conformal vertex algebras give rise to sheaves of coinvariants and conformal blocks on moduli of stable pointed curves. Here we prove the factorization conjecture for these sheaves. Our results apply in arbitrary genus and for a large class of vertex algebras. As an application, sheaves defined by finitely generated admissible modules over vertex algebras satisfying natural hypotheses are shown to be vector bundles. Factorization is essential to a recursive formulation of invariants, like ranks and Chern classes, and to produce new constructions of rational conformal field theories and cohomological field theories.

  PublisherDOI

• Conformal blocks on smoothings via mode transition algebras

  arXiv (Cornell University) · 2023-07-07

  preprintOpen access

  Here we define a series of associative algebras attached to a vertex operator algebra $V$, called mode transition algebras, showing they reflect both algebraic properties of $V$ and geometric constructions on moduli of curves. One can define sheaves of coinvariants on pointed coordinatized curves from $V$-modules. We show that if the mode transition algebras admit multiplicative identities with certain properties, these sheaves deform as wanted on families of curves with nodes (so $V$ satisfies smoothing). Consequently, coherent sheaves of coinvariants defined by vertex operator algebras that satisfy smoothing form vector bundles. We also show that mode transition algebras give information about higher level Zhu algebras and generalized Verma modules. As an application, we completely describe higher level Zhu algebras of the Heisenberg vertex algebra for all levels, proving a conjecture of Addabbo--Barron.

  PublisherOA PDFDOI

• On global generation of vector bundles on the moduli space of curves from representations of \n vertex operator algebras

  Algebraic geometry · 2023-04-21 · 3 citations

  articleOpen accessSenior author

  We consider global generation of sheaves of coinvariants on moduli of curves given by simple modules over certain vertex operator algebras, extending results for affine vertex operator algebras at integrable levels on stable pointed rational curves.A number of examples illustrate the subtlety of the problem.certain W -algebras, even lattice VOAs, and holomorphic VOAs (like the moonshine module), and others obtained as tensor products, orbifold algebras, and through coset constructions.Affine VOAs are derived from (quotients of) the affinization of a Lie algebra g, and ℓ ∈ C, with -ℓ not equal to the dual Coxeter number.The simple affine VOA L ℓ (g), generated by its degree 1 component g, is strongly rational if and only if ℓ ∈ Z >0 .For g reductive, V g (L ℓ (g); W • ) was shown to be a vector bundle on M g,n in [TUY89] and globally generated on M 0,n in [Fak12].In this work, we investigate global generation in a more general context.Our main result is the following.Theorem 1. Sheaves of coinvariants defined by simple admissible modules over a vertex operator algebra, strongly generated in degree 1, are globally generated on J 0,n , and on M 0,n if defined.Here we assume that all VOAs are of CFT-type.

  PublisherDOI

• 1. Our Early Career, Looking Back by Angela Gibney

  Notices of the American Mathematical Society · 2022-01-01

  article1st authorCorresponding
  PublisherDOI

• Vertex Algebras of CohFT-type

  Cambridge University Press eBooks · 2022-03-14 · 10 citations

  book-chapter

  A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.

  PublisherDOI

• Factorization presentations

  arXiv (Cornell University) · 2022-07-11 · 1 citations

  preprintOpen access

  Modules over a vertex operator algebra V give rise to sheaves of coinvariants on moduli of stable pointed curves. If V satisfies finiteness and semi-simplicity conditions, these sheaves are vector bundles. This relies on factorization, an isomorphism of spaces of coinvariants at a nodal curve with a finite sum of analogous spaces on the normalization of the curve. Here we introduce the notion of a factorization presentation, and using this, we show that finiteness conditions on V imply the sheaves of coinvariants are coherent on moduli spaces of pointed stable curves without any assumption of semisimplicity.

  PublisherOA PDFDOI

Recent grants

• Vector Bundles of Conformal Blocks on Moduli Spaces

  NSF · $136k · 2016–2018

• Vector Bundles of Conformal Blocks on Moduli Spaces

  NSF · $92k · 2017–2020

• The Birational Geometry of Moduli Spaces of Curves

  NSF · $84k · 2004–2008

• Conformal blocks and positive cycles on the moduli space of curves

  NSF · $111k · 2012–2016

Frequent coauthors

• David Swinarski

  16 shared

• Prakash Belkale

  14 shared

• Chiara Damiolini

  12 shared

• Daniel Krashen

  11 shared

• Han-Bom Moon

  10 shared

• David Jensen

  University of Kentucky

  10 shared

• Nick Sevdalis

  National University of Singapore

  7 shared

• Swarnava Mukhopadhyay

  Tata Institute of Fundamental Research

  7 shared

Education

• Ph.D., Mathematics

  The University of Texas at Austin

  2000

• B.S., Mathematics

  University of California Santa Barbara

  1995

• Masterclass in Algebraic Geometry, Mathematical Institute

  Utrecht University

  1994