Duncan, John F. R.
Research Fellow
Research Fields: Moonshine, vertex algebra, finite simple groups, automorphic forms, arithmetic of algebraic varieties, conformal field theory, quantum gravity,
Email : jduncan@gate.sinica.edu.tw
Extension : 738
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
- (with Miranda C. N. Cheng and Michael H. Mertens) "Class Numbers, Congruent Numbers and Umbral Moonshine", arXiv, 2023, Link
- (with Miranda C. N. Cheng and Michael H. Mertens) "Class Numbers, Cyclic Simple Groups and Arithmetic", Journal of the London Mathematical Society, 2022, Link
- (with Jeffrey A. Harvey and Brandon C. Rayhaun) "Two New Avatars of Moonshine for the Thompson Group", arXiv, 2022, Link
- (with Jeffrey A. Harvey and Brandon C. Rayhaun) "Modular Products and Modules for Finite Groups", Algebras and Representation Theory, 2022, Link
- (with Jeffrey A. Harvey and Brandon C. Rayhaun) "An Overview of Penumbral Moonshine", arXiv, 2021, Link
- (with Vassilis Anagiannis, Miranda C. N. Cheng, and Roberto Volpato) "Vertex operator superalgebra/sigma model correspondences: The four-torus case", Progress of Theoretical and Experimental Physics, 2021 (8), 2021, Link
- (with Miranda C. N. Cheng) "Optimal Mock Jacobi Theta Functions", Advances in Mathematics, 372, 2020, Link
- "A Short Introduction to the Algebra, Geometry, Number Theory and Physics of Moonshine", Partition Functions and Automorphic Forms, 2020
- (with David A. McGady) "Modular Forms on the Double Half-Plane", International Journal of Number Theory, 16 (09 ), 1989-2003, 2020, Link
- "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
- (with Miranda C. N. Cheng) "Meromorphic Jacobi Forms of Half-Integral Index and Umbral Moonshine Modules", Communications in Mathematical Physics, 370 (3), 759-780, 2019, Link
- (with Andrew O’Desky) "Super vertex algebras, meromorphic Jacobi forms and umbral moonshine", J. Algebra, 515, 389-407, 2018, Link
- (with Miranda C. N. Cheng, Sarah M. Harrison, Jeffrey A. Harvey, Shamit Kachru and Brandon C. Rayhaun) "Attractive Strings and Five-Branes, Skew-Holomorphic Jacobi Forms and Moonshine", J. High Energy Physics, 130, 2018, Link
- (with Miranda C. N. Cheng and Jeffrey A. Harvey) "Weight One Jacobi Forms and Umbral Moonshine", J. Phys. A: Math. Theor, 51, 2018
- (with Thomas Creutzig and Wolfgang Riedler) "Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory", J. Phys. A: Math. Theor, 51, 2018, Link
- (with Michael H. Mertens and Ken Ono) "O’Nan Moonshine and Arithmetic", American Journal of Mathematics, 2017, Link
- (with Michael H. Mertens and Ken Ono) "Pariah moonshine", Nature Communications, 8 (1), 2017, Link
- (with Miranda C. N. Cheng, Sarah Harrison and Shamit Kachru) "Equivariant K3 Invariants", Communications in Number Theory and Physics, 11 (1), 2017, Link
- (with Jeffrey A. Harvey) "The Umbral Moonshine Module for the Unique Unimodular Niemeier Root System", Algebra and Number Theory, 11 (3), 505-535, 2017, Link
- (with Ken Ono) "The Jack Daniels Problem", Journal of Number Theory, 161, 230-239, 2016-04 , Link
- (with Sander MackCrane) "Derived Equivalences of K3 Surfaces and Twined Elliptic Genera", Research in the Mathematical Sciences, 3, 2016, Link
- (with Michael Griffin and Ken Ono) "Proof of the Umbral Moonshine Conjecture", Research in the Mathematical Sciences, 2, 2015, Link
- (with Michael Griffin and Ken Ono) "Moonshine", Research in the Mathematical Sciences, 2, 2015, Link
- (with Kathrin Bringmann and Larry Rolen) "Maass-Jacobi Poincar´e Series and Mathieu Moonshine", Advances in Mathematics, 281, 248-278, 2015, Link
- (with Sander Mack-Crane) "The Moonshine Module for Conway’s Group", Forum of Mathematics, Sigma, 3, 2015, Link
- (with 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
- (with 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
- (with Miranda C. N. Cheng) "On the Discrete Groups of Mathieu Moonshine", Perspectives in Representation Theory, Contemporary Mathematics, 610, 2014, Link
- (with 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
- (with 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
- (with Miranda C. N. Cheng and Jeffrey A. Harvey) "Umbral Moonshine", Communications in Number Theory and Physics, 8 (2), 101-242, 2014, Link
- (with 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
- (with Miranda C. N. Cheng) "The Largest Mathieu Group and (Mock) Automorphic Forms", String-Math 2011, Proceedings of Symposia in Pure Mathematics, 85, 2012, Link
- (with 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
- (with Christopher J. Cummins) "An E8 correspondence for multiplicative eta-products", Canadian Mathematical Bulletin, 55, 67-72, 2012, Link
- (with 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