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)

**Links**

**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**

- (with Miranda C. N. Cheng and Michael H. Mertens) "Class Numbers, Cyclic Simple Groups and Arithmetic"
,
*arXiv*, 2022. (preprint) - (with Jeffrey A. Harvey and Brandon C. Rayhaun) "Two New Avatars of Moonshine for the Thompson Group"
,
*arXiv*, 2022. (preprint) - (with Jeffrey A. Harvey and Brandon C. Rayhaun) "Modular Products and Modules for Finite Groups"
,
*arXiv*, 2022. (preprint) - (with Jeffrey A. Harvey and Brandon C. Rayhaun) "An Overview of Penumbral Moonshine"
,
*arXiv*, 2021. (preprint) - (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. - (with Miranda C. N. Cheng) "Optimal Mock Jacobi Theta Functions"
,
*Advances in Mathematics*, 372, 2020. - "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. - "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. - (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. - (with Andrew O’Desky) "Super vertex algebras, meromorphic Jacobi forms and umbral moonshine"
,
*J. Algebra*, 515, 389-407, 2018. - (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. - (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. - (with Michael H. Mertens and Ken Ono) "O’Nan Moonshine and Arithmetic"
,
*American Journal of Mathematics*, 2017. - (with Michael H. Mertens and Ken Ono) "Pariah moonshine"
,
*Nature Communications*, 8 (1), 2017. - (with Miranda C. N. Cheng, Sarah Harrison and Shamit Kachru) "Equivariant K3 Invariants"
,
*Communications in Number Theory and Physics*, 11 (1), 2017. - (with Jeffrey A. Harvey) "The Umbral Moonshine Module for the Unique Unimodular Niemeier Root System"
,
*Algebra and Number Theory*, 11 (3), 505-535, 2017. - (with Ken Ono) "The Jack Daniels Problem"
,
*Journal of Number Theory*, 161, 230-239, 2016-04. - (with Sander MackCrane) "Derived Equivalences of K3 Surfaces and Twined Elliptic Genera"
,
*Research in the Mathematical Sciences*, 3:1, 2016. - (with Michael Griffin and Ken Ono) "Proof of the Umbral Moonshine Conjecture"
,
*Research in the Mathematical Sciences*, 2:16, 2015. - (with Michael Griffin and Ken Ono) "Moonshine"
,
*Research in the Mathematical Sciences*, 2:11, 2015. - (with Kathrin Bringmann and Larry Rolen) "Maass-Jacobi Poincar´e Series and Mathieu Moonshine"
,
*Advances in Mathematics*, 281, 248-278, 2015. - (with Sander Mack-Crane) "The Moonshine Module for Conway’s Group"
,
*Forum of Mathematics, Sigma*, 3, 2015. - (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. - (with Miranda C. N. Cheng and Jeffrey A. Harvey) "Umbral Moonshine and the Niemeier Lattices"
,
*Research in the Mathematical Sciences*, 1:3, 2014. - "Umbral Moonshine and Linear Codes"
,
*RIMS Kôkyûroku*(1872), 2014. - (with Miranda C. N. Cheng) "On the Discrete Groups of Mathieu Moonshine"
,
*Perspectives in Representation Theory, Contemporary Mathematics*, 610, 2014. - (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. - (with Miranda C. N. Cheng and Jeffrey A. Harvey) "Umbral Moonshine"
,
*Communications in Number Theory and Physics*, 8 (2), 101-242, 2014. - (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. - (with Miranda C. N. Cheng) "The Largest Mathieu Group and (Mock) Automorphic Forms"
,
*String-Math 2011, Proceedings of Symposia in Pure Mathematics*, 85, 2012. - (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. - (with Christopher J. Cummins) "An E8 correspondence for multiplicative eta-products"
,
*Canadian Mathematical Bulletin*, 55, 67-72, 2012. - (with Igor B. Frenkel) "Rademacher sums, moonshine and gravity"
,
*Communications in Number Theory and Physics*, 5 (4), 849-976, 2011. - "Vertex operators and sporadic groups"
,
*Moonshine - The First Quarter Century and Beyond*, 2010. - "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. - "Super-moonshine for Conway’s largest sporadic group"
,
*Duke Math. J.*, 139 (2), 255-315, 2007.

Director & Deputy Director