The focus of my work is moonshine, and involves aspects of number theory, algebra, geometry and mathematical physics.
- Ph.D. in Mathematics Yale University 2001 - 2006
- M. S. University of Auckland, Wellington, New Zealand 1999 - 2001
- Associate Professor Emory University 2018/9 - 2021
- Assistant Professor Emory University 2015/7 - 2018/8
- Project Associate Professor Tokyo University, Japan 2015/5 - 2015/8
- Assistant Professor (tenure track) Case Western Reserve University 2010/10 - 2015/6
- Junior Research Fellow King’s College, Cambridge, U.K 2009/10 - 2010/9
- Benjamin Peirce Lecturer on Mathematics Harvard University 2006/7 - 2009/6
- John F. R. Duncan and Holly Swisher, "Modular Functions and the Monstrous Exponents", arXiv, 2026, Link , Link
- John F. R. Duncan, Jeffrey A. Harvey, Brandon C. Rayhaun, "An Overview of Penumbral Moonshine", Communications in Number Theory and Physics, 20 (1), 1-95, 2026, Link , Link, Link
- Federico Carta, John F. R. Duncan and Yang-Hui He, "Rational K3 Homotopy and the Largest Mathieu Group", arXiv, 2025, Link , Link
- John F. R. Duncan, "A Guide to Moonshine", Bulletin of the Institute of Mathematics Academia Sinica (New Series), 20 (3), 215-237, 2025, Link , Link
- Miranda C. N. Cheng, John F. R. Duncan and Michael H. Mertens, "Class Numbers, Congruent Numbers and Umbral Moonshine", Journal of Number Theory, 277 (December 2025), 201-235, 2025, Link , Link
- John F. R. Duncan, Jeffrey A. Harvey, Brandon C. Rayhaun, "Two New Avatars of Moonshine for the Thompson Group", Bulletin of the Institute of Mathematics Academia Sinica (New Series), 20 (4 ), 239-333, 2025, Link , Link, Link
- John F. R. Duncan, Jeffrey A. Harvey and Brandon C. Rayhaun, "Modular Products and Modules for Finite Groups", Algebras and Representation Theory, 27, 115-159, 2024 , Link
- Miranda C. N. Cheng, John F. R. Duncan and Michael H. Mertens, "Class Numbers, Cyclic Simple Groups and Arithmetic", Journal of the London Mathematical Society, 108 (1), 238-272, 2023 , Link
- Vassilis Anagiannis, Miranda C. N. Cheng, John F. R. Duncan and Roberto Volpato, "Vertex operator superalgebra/sigma model correspondences: The four-torus case", Progress of Theoretical and Experimental Physics, 2021 (8), 2021 , Link
- Miranda C. N. Cheng and John F. R. Duncan, "Optimal Mock Jacobi Theta Functions", Advances in Mathematics, 372, 2020 , Link
- John F. R. Duncan, "A Short Introduction to the Algebra, Geometry, Number Theory and Physics of Moonshine", Partition Functions and Automorphic Forms, 2020
- John F. R. Duncan and David A. McGady, "Modular Forms on the Double Half-Plane", International Journal of Number Theory, 16 (09 ), 1989-2003, 2020 , Link
- John F. R. Duncan, "From the Monster to Thompson to O’Nan", Proceedings of the Conference on Vertex Operator Algebras, Number Theory and Related Topics, Contemporary Mathematics, 753, 2020 , Link
- Miranda C. N. Cheng, John F. R. Duncan, "Meromorphic Jacobi Forms of Half-Integral Index and Umbral Moonshine Modules", Communications in Mathematical Physics, 370 (3), 759-780, 2019 , Link
- John F. R. Duncan, Andrew O'Desky, "Super vertex algebras, meromorphic Jacobi forms and umbral moonshine", J. Algebra, 515, 389-407, 2018 , Link
- Miranda C.N. Cheng, John F.R. Duncan, Sarah M. Harrison, Jeffrey A. Harvey, Shamit Kachru, Brandon C. Rayhaun, "Attractive Strings and Five-Branes, Skew-Holomorphic Jacobi Forms and Moonshine", J. High Energy Physics, 130, 2018 , Link
- Miranda C. N. Cheng, John F. R. Duncan, Jeffrey A. Harvey, "Weight One Jacobi Forms and Umbral Moonshine", J. Phys. A: Math. Theor, 51, 2018
- Thomas Creutzig, John F. R. Duncan, Wolfgang Riedler, "Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory", J. Phys. A: Math. Theor, 51, 2018 , Link
- John F. R. Duncan, Michael H. Mertens, Ken Ono, "O’Nan Moonshine and Arithmetic", American Journal of Mathematics, 2017 , Link
- John F. R. Duncan, Michael H. Mertens, Ken Ono, "Pariah moonshine", Nature Communications, 8 (1), 2017 , Link
- Miranda C. N. Cheng, John F. R. Duncan, Sarah M. Harrison, Shamit Kachru, "Equivariant K3 Invariants", Communications in Number Theory and Physics, 11 (1), 2017 , Link
- John F. R. Duncan, Jeffrey A. Harvey, "The Umbral Moonshine Module for the Unique Unimodular Niemeier Root System", Algebra and Number Theory, 11 (3), 505-535, 2017 , Link
- John F. R. Duncan, Ken Ono, "The Jack Daniels Problem", Journal of Number Theory, 161, 230-239, 2016-04 , Link
- Sander MackCrane, "Derived Equivalences of K3 Surfaces and Twined Elliptic Genera", Research in the Mathematical Sciences, 3, 2016 , Link
- Michael Griffin and Ken Ono, "Proof of the Umbral Moonshine Conjecture", Research in the Mathematical Sciences, 2, 2015 , Link
- Michael Griffin and Ken Ono, "Moonshine", Research in the Mathematical Sciences, 2, 2015 , Link
- Kathrin Bringmann and Larry Rolen, "Maass-Jacobi Poincar´e Series and Mathieu Moonshine", Advances in Mathematics, 281, 248-278, 2015 , Link
- Sander Mack-Crane, "The Moonshine Module for Conway’s Group", Forum of Mathematics, Sigma, 3, 2015 , Link
- Miranda C. N. Cheng, Xi Dong, Sarah Harrison, Shamit Kachru and Timm Wrase, "Mock Modular Mathieu Moonshine Modules", Research in the Mathematical Sciences, 2, 2015 , Link
- Miranda C. N. Cheng and Jeffrey A. Harvey, "Umbral Moonshine and the Niemeier Lattices", Research in the Mathematical Sciences, 1, 2014 , Link
- "Umbral Moonshine and Linear Codes", RIMS Kôkyûroku, 2014
- Miranda C. N. Cheng, "On the Discrete Groups of Mathieu Moonshine", Perspectives in Representation Theory, Contemporary Mathematics, 610, 2014 , Link
- Pavel Etingof, Ivan Ip, Mikhail Khovanov, Matvei Libine, Anthony Licata, Alistair Savage and Michael Schlosser, "On the work of Igor Frenkel", Perspectives in Representation Theory, Contemporary Mathematics, 610, 2014
- Miranda C. N. Cheng, "Rademacher Sums and Rademacher Series", Conformal Field Theory, Automorphic Forms and Related Topics, Contributions in Mathematical and Computational Sciences, 8, 143-182, 2014 , Link
- Miranda C. N. Cheng and Jeffrey A. Harvey, "Umbral Moonshine", Communications in Number Theory and Physics, 8 (2), 101-242, 2014 , Link
- Miranda C. N. Cheng, Xi Dong, Jeffrey A. Harvey, Shamit Kachru and Timm Wrase, "Mathieu Moonshine and N = 2 String Compactifications", Journal of High Energy Physics, 9, 2013 , Link
- Miranda C. N. Cheng, "The Largest Mathieu Group and (Mock) Automorphic Forms", String-Math 2011, Proceedings of Symposia in Pure Mathematics, 85, 2012 , Link
- Miranda C. N. Cheng, "On Rademacher Sums, the Largest Mathieu Group, and the Holographic Modularity of Moonshine", Communications in Number Theory and Physics, 6 (3), 697-758, 2012 , Link
- Christopher J. Cummins, "An E8 correspondence for multiplicative eta-products", Canadian Mathematical Bulletin, 55, 67-72, 2012 , Link
- Igor B. Frenkel, "Rademacher sums, moonshine and gravity", Communications in Number Theory and Physics, 5 (4), 849-976, 2011 , Link
- "Vertex operators and sporadic groups", Moonshine - The First Quarter Century and Beyond, 2010 , Link
- "Extensions of the Virasoro algebra", Lie Theory and its Applications in Physics VII, 431-438, 2008
- "Arithmetic groups and the affine E8 Dynkin diagram", CRM Proceedings and Lecture Notes, 47, 2008 , Link
- "Super-moonshine for Conway’s largest sporadic group", Duke Math. J., 139 (2), 255-315, 2007 , Link