Research Fellow |   Duncan, John F. R.
Contact Information
• jduncan$\color{red}{@}$gate.sinica.edu.tw
• +886 2 2368-5999 ext. 738
• +886 2 2368-9771
Research Interests
• Moonshine
• vertex algebra
• finite simple groups
• automorphic forms
• arithmetic of algebraic varieties
• conformal field theory
• quantum gravity
Education
• Ph.D. in Mathematics Yale University (2001 - 2006)
• M. S. University of Auckland, Wellington, New Zealand (1999 - 2001)

Work Experience
• 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

Research Descriptions

The focus of my work is moonshine, and involves aspects of number theory, algebra, geometry and mathematical physics.

Selected Publications
1. (with Miranda C. N. Cheng and Michael H. Mertens) "Class Numbers, Cyclic Simple Groups and Arithmetic" , arXiv , 2022. (preprint)
2. (with Jeffrey A. Harvey and Brandon C. Rayhaun) "Two New Avatars of Moonshine for the Thompson Group" , arXiv , 2022. (preprint)
3. (with Jeffrey A. Harvey and Brandon C. Rayhaun) "Modular Products and Modules for Finite Groups" , arXiv , 2022. (preprint)
4. (with Jeffrey A. Harvey and Brandon C. Rayhaun) "An Overview of Penumbral Moonshine" , arXiv , 2021. (preprint)
5. (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.
6. (with Miranda C. N. Cheng) "Optimal Mock Jacobi Theta Functions" , Advances in Mathematics , 372, 2020.
7. "A Short Introduction to the Algebra, Geometry, Number Theory and Physics of Moonshine" , Partition Functions and Automorphic Forms , 2020.
8. (with David A. McGady) "Modular Forms on the Double Half-Plane" , International Journal of Number Theory , 16 (09), 1989-2003, 2020.
9. "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.
10. (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.
11. (with Andrew O’Desky) "Super vertex algebras, meromorphic Jacobi forms and umbral moonshine" , J. Algebra , 515, 389-407, 2018.
12. (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.
13. (with Miranda C. N. Cheng and Jeffrey A. Harvey) "Weight One Jacobi Forms and Umbral Moonshine" , J. Phys. A: Math. Theor , 51, 2018.
14. (with Thomas Creutzig and Wolfgang Riedler) "Self-Dual Vertex Operator Superalgebras and Superconformal Field Theory" , J. Phys. A: Math. Theor , 51, 2018.
15. (with Michael H. Mertens and Ken Ono) "O’Nan Moonshine and Arithmetic" , American Journal of Mathematics , 2017.
16. (with Michael H. Mertens and Ken Ono) "Pariah moonshine" , Nature Communications , 8 (1), 2017.
17. (with Miranda C. N. Cheng, Sarah Harrison and Shamit Kachru) "Equivariant K3 Invariants" , Communications in Number Theory and Physics , 11 (1), 2017.
18. (with Jeffrey A. Harvey) "The Umbral Moonshine Module for the Unique Unimodular Niemeier Root System" , Algebra and Number Theory , 11 (3), 505-535, 2017.
19. (with Ken Ono) "The Jack Daniels Problem" , Journal of Number Theory , 161, 230-239, 2016-04.
20. (with Sander MackCrane) "Derived Equivalences of K3 Surfaces and Twined Elliptic Genera" , Research in the Mathematical Sciences , 3:1, 2016.
21. (with Michael Griffin and Ken Ono) "Proof of the Umbral Moonshine Conjecture" , Research in the Mathematical Sciences , 2:16, 2015.
22. (with Michael Griffin and Ken Ono) "Moonshine" , Research in the Mathematical Sciences , 2:11, 2015.
23. (with Kathrin Bringmann and Larry Rolen) "Maass-Jacobi Poincar´e Series and Mathieu Moonshine" , Advances in Mathematics , 281, 248-278, 2015.
24. (with Sander Mack-Crane) "The Moonshine Module for Conway’s Group" , Forum of Mathematics, Sigma , 3, 2015.
25. (with Miranda C. N. Cheng, Xi Dong, Sarah Harrison, Shamit Kachru and Timm Wrase) "Mock Modular Mathieu Moonshine Modules" , Research in the Mathematical Sciences , 2:13, 2015.
26. (with Miranda C. N. Cheng and Jeffrey A. Harvey) "Umbral Moonshine and the Niemeier Lattices" , Research in the Mathematical Sciences , 1:3, 2014.
27. "Umbral Moonshine and Linear Codes" , RIMS Kôkyûroku (1872), 2014.
28. (with Miranda C. N. Cheng) "On the Discrete Groups of Mathieu Moonshine" , Perspectives in Representation Theory, Contemporary Mathematics , 610, 2014.
29. (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.
30. (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.
31. (with Miranda C. N. Cheng and Jeffrey A. Harvey) "Umbral Moonshine" , Communications in Number Theory and Physics , 8 (2), 101-242, 2014.
32. (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 , 09, 2013.
33. (with Miranda C. N. Cheng) "The Largest Mathieu Group and (Mock) Automorphic Forms" , String-Math 2011, Proceedings of Symposia in Pure Mathematics , 85, 2012.
34. (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.
35. (with Christopher J. Cummins) "An E8 correspondence for multiplicative eta-products" , Canadian Mathematical Bulletin , 55, 67-72, 2012.
36. (with Igor B. Frenkel) "Rademacher sums, moonshine and gravity" , Communications in Number Theory and Physics , 5 (4), 849-976, 2011.
37. "Vertex operators and sporadic groups" , Moonshine - The First Quarter Century and Beyond , 2010.
38. "Extensions of the Virasoro algebra" , Lie Theory and its Applications in Physics VII , 431-438, 2008.
39. "Arithmetic groups and the affine E8 Dynkin diagram" , CRM Proceedings and Lecture Notes , 47, 2008.
40. "Super-moonshine for Conway’s largest sporadic group" , Duke Math. J. , 139 (2), 255-315, 2007.