John F. R. Duncan
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
John F. R. Duncan has a total of 32 co-authors. Here are the top co-authors by number of shared publications:
- Miranda C. N. Cheng
Institute of Physics University of Amsterdam Netherlands
8 shared publications - Jeffrey A. Harvey
University of Chicago
7 shared publications - Miranda C. N. Cheng
UMR CNRS 7586 Université Paris 7 Paris France
7 shared publications - Colin M. McGregor
Department of Mathematics University of Glasgow G12 8QW Glasgow Scotland UK
6 shared publications - Ken Ono
Department of Mathematics, University of Virginia, Charlottesville, USA
5 shared publications - Shamit Kachru
Stanford Institute for Theoretical Physics, Stanford University, Stanford, USA
4 shared publications
Latest Publications
- Open Access
- 1 August 2021
- Published by Oxford University Press (OUP) in Progress of Theoretical and Experimental Physics
- Vol. 2021 (8)
Vertex operator superalgebra/sigma model correspondences: The four-torus case
We propose a correspondence between vertex operator superalgebras and families of sigma models in which the two structures are related by symmetry properties and a certain reflection procedure. The existence of such a correspondence is motivated by previous work on ${\cal N}=(4,4)$ supersymmetric non-linear sigma models on K3 surfaces, and on a vertex operator superalgebra with Conway group symmetry. Here we present an example of the correspondence for ${\cal N}=(4,4)$ supersymmetric non-linear sigma models on four-tori, and compare it to the K3 case.- 1 August 2021
- Published by Oxford University Press (OUP) in Progress of Theoretical and Experimental Physics
- Vol. 2021 (8)
Open AccessVertex operator superalgebra/sigma model correspondences: The four-torus case
We propose a correspondence between vertex operator superalgebras and families of sigma models in which the two structures are related by symmetry properties and a certain reflection procedure. The existence of such a correspondence is motivated by previous work on ${\cal N}=(4,4)$ supersymmetric non-linear sigma models on K3 surfaces, and on a vertex operator superalgebra with Conway group symmetry. Here we present an example of the correspondence for ${\cal N}=(4,4)$ supersymmetric non-linear sigma models on four-tori, and compare it to the K3 case. - 10 June 2021
- Published by Cambridge University Press (CUP) in Glasgow Mathematical Journal
- Vol. 64 (2) , 376-396
HERMITIANS IN MATRIX ALGEBRAS WITH OPERATOR NORM – II
We continue our investigation of the real space H of Hermitian matrices in $${M_n}(\mathbb{C})$$ with respect to norms on $${\mathbb{C}^n}$$ . We complete the commutative case by showing that any proper real subspace of the real diagonal matrices on $${\mathbb{C}^n}$$ can appear as H. For the non-commutative case, we give a complete solution when n=3 and we provide various illustrative examples for n ≥ 4. We end with a short list of problems.- 10 June 2021
- Published by Cambridge University Press (CUP) in Glasgow Mathematical Journal
- Vol. 64 (2) , 376-396
HERMITIANS IN MATRIX ALGEBRAS WITH OPERATOR NORM – II
We continue our investigation of the real space H of Hermitian matrices in $${M_n}(\mathbb{C})$$ with respect to norms on $${\mathbb{C}^n}$$ . We complete the commutative case by showing that any proper real subspace of the real diagonal matrices on $${\mathbb{C}^n}$$ can appear as H. For the non-commutative case, we give a complete solution when n=3 and we provide various illustrative examples for n ≥ 4. We end with a short list of problems.- 10 July 2020
- Published by Springer Nature
- p. 1-85
A Short Introduction to the Algebra, Geometry, Number Theory and Physics of Moonshine
- 10 July 2020
- Published by Springer Nature
- p. 1-85
A Short Introduction to the Algebra, Geometry, Number Theory and Physics of Moonshine
- 27 April 2020
- Published by Cambridge University Press (CUP) in Glasgow Mathematical Journal
- Vol. 63 (2) , 280-290
HERMITIANS IN MATRIX ALGEBRAS WITH OPERATOR NORM
We investigate the real space H of Hermitian matrices in $M_n(\mathbb{C})$ with respect to norms on $\mathbb{C}^n$ . For absolute norms, the general form of Hermitian matrices was essentially established by Schneider and Turner [Schneider and Turner, Linear and Multilinear Algebra (1973), 9–31]. Here, we offer a much shorter proof. For non-absolute norms, we begin an investigation of H by means of a series of examples, with particular reference to dimension and commutativity.- 27 April 2020
- Published by Cambridge University Press (CUP) in Glasgow Mathematical Journal
- Vol. 63 (2) , 280-290
HERMITIANS IN MATRIX ALGEBRAS WITH OPERATOR NORM
We investigate the real space H of Hermitian matrices in $M_n(\mathbb{C})$ with respect to norms on $\mathbb{C}^n$ . For absolute norms, the general form of Hermitian matrices was essentially established by Schneider and Turner [Schneider and Turner, Linear and Multilinear Algebra (1973), 9–31]. Here, we offer a much shorter proof. For non-absolute norms, we begin an investigation of H by means of a series of examples, with particular reference to dimension and commutativity.- Open Access
Modular Forms on the Double Half-Plane
We formulate a notion of modular form on the double half-plane for half-integral weights and explain its relationship to the usual notion of modular form. The construction we provide is compatible with certain physical considerations due to the second author.
Open AccessModular Forms on the Double Half-Plane
We formulate a notion of modular form on the double half-plane for half-integral weights and explain its relationship to the usual notion of modular form. The construction we provide is compatible with certain physical considerations due to the second author.
- 1 January 2020
- Published by American Mathematical Society (AMS)
- Vol. 753, 73-93
From the Monster to Thompson to O’Nan
The commencement of monstrous moonshine is a connection between the largest sporadic simple group—the monster—and complex elliptic curves. Here we explain how a closer look at this connection leads, via the Thompson group, to recently observed relationships between the non-monstrous sporadic simple group of O’Nan and certain families of elliptic curves defined over the rationals. We also describe umbral moonshine from this perspective.
- 1 January 2020
- Published by American Mathematical Society (AMS)
- Vol. 753, 73-93
From the Monster to Thompson to O’Nan
The commencement of monstrous moonshine is a connection between the largest sporadic simple group—the monster—and complex elliptic curves. Here we explain how a closer look at this connection leads, via the Thompson group, to recently observed relationships between the non-monstrous sporadic simple group of O’Nan and certain families of elliptic curves defined over the rationals. We also describe umbral moonshine from this perspective.
- Open Access
From the Monster to Thompson to O'Nan
The commencement of monstrous moonshine is a connection between the largest sporadic simple group---the monster---and complex elliptic curves. Here we explain how a closer look at this connection leads, via the Thompson group, to recently observed relationships between the non-monstrous sporadic simple group of O'Nan and certain families of elliptic curves defined over the rationals. We also describe umbral moonshine from this perspective.
Open AccessFrom the Monster to Thompson to O'Nan
The commencement of monstrous moonshine is a connection between the largest sporadic simple group---the monster---and complex elliptic curves. Here we explain how a closer look at this connection leads, via the Thompson group, to recently observed relationships between the non-monstrous sporadic simple group of O'Nan and certain families of elliptic curves defined over the rationals. We also describe umbral moonshine from this perspective.
- 10 August 2019
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 370 (3) , 759-780
Meromorphic Jacobi Forms of Half-Integral Index and Umbral Moonshine Modules
- 10 August 2019
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 370 (3) , 759-780
Meromorphic Jacobi Forms of Half-Integral Index and Umbral Moonshine Modules
- Open Access
Super Vertex Algebras, Meromorphic Jacobi Forms and Umbral Moonshine
The vector-valued mock modular forms of umbral moonshine may be repackaged into meromorphic Jacobi forms of weight one. In this work we constructively solve two cases of the meromorphic module problem for umbral moonshine. Specifically, for the type A Niemeier root systems with Coxeter numbers seven and thirteen, we construct corresponding bigraded super vertex operator algebras, equip them with actions of the corresponding umbral groups, and verify that the resulting trace functions on canonically twisted modules recover the meromorphic Jacobi forms that are specified by umbral moonshine. We also obtain partial solutions to the meromorphic module problem for the type A Niemeier root systems with Coxeter numbers four and five, by constructing super vertex operator algebras that recover the meromorphic Jacobi forms attached to maximal subgroups of the corresponding umbral groups.
Open AccessSuper Vertex Algebras, Meromorphic Jacobi Forms and Umbral Moonshine
The vector-valued mock modular forms of umbral moonshine may be repackaged into meromorphic Jacobi forms of weight one. In this work we constructively solve two cases of the meromorphic module problem for umbral moonshine. Specifically, for the type A Niemeier root systems with Coxeter numbers seven and thirteen, we construct corresponding bigraded super vertex operator algebras, equip them with actions of the corresponding umbral groups, and verify that the resulting trace functions on canonically twisted modules recover the meromorphic Jacobi forms that are specified by umbral moonshine. We also obtain partial solutions to the meromorphic module problem for the type A Niemeier root systems with Coxeter numbers four and five, by constructing super vertex operator algebras that recover the meromorphic Jacobi forms attached to maximal subgroups of the corresponding umbral groups.
- Open Access
O'Nan moonshine and arithmetic
Answering a question posed by Conway and Norton in their seminal 1979 paper on moonshine, we prove the existence of a graded infinite-dimensional module for the sporadic simple group of O'Nan, for which the McKay--Thompson series are weight $3/2$ modular forms. The coefficients of these series may be expressed in terms of class numbers, traces of singular moduli, and central critical values of quadratic twists of weight 2 modular $L$-functions. As a consequence, for primes $p$ dividing the order of the O'Nan group we obtain congruences between O'Nan group character values and class numbers, $p$-parts of Selmer groups, and Tate--Shafarevich groups of certain elliptic curves. This work represents the first example of moonshine involving arithmetic invariants of this type.Open AccessO'Nan moonshine and arithmetic
Answering a question posed by Conway and Norton in their seminal 1979 paper on moonshine, we prove the existence of a graded infinite-dimensional module for the sporadic simple group of O'Nan, for which the McKay--Thompson series are weight $3/2$ modular forms. The coefficients of these series may be expressed in terms of class numbers, traces of singular moduli, and central critical values of quadratic twists of weight 2 modular $L$-functions. As a consequence, for primes $p$ dividing the order of the O'Nan group we obtain congruences between O'Nan group character values and class numbers, $p$-parts of Selmer groups, and Tate--Shafarevich groups of certain elliptic curves. This work represents the first example of moonshine involving arithmetic invariants of this type.